Jai alai, a quick-tempo Spanish court game that is the subject of game-fixing investigations in two of the four states where it is played, is the most controversial proposal on the May 6 referendum that would legalize some forms of gambling in the District of Columbia.

Gambling opponents, contending that more crime, longer welfare rolls and increasing social problems would accompany legal wagering in the nation's capital, are focusing much of their campaign on jai alai.

They say the questionable operation of the game in other states is the best argument against passage of the D.C. referendum, an all-or-nothing proposition that would also legalize parimutuel wagering on dog racing, a city-run daily numbers game, bingo, raffles and social betting such as poker. a

"The poor man who can ill afford to lose money is the victim [of jai alai]," said the Rev. Raymond Robinson, pastor of Israel Baptist Church in Northeast Washington and chairman of the Committee of 100 Ministers. "I would hate to see our nation's capital turned into a gambling capital."

Gambling proponents, asserting that the financially troubled city government could raise nearly $4 million a year if jai alai were permitted in the District of Columbia, said there is no reason to bar the sport in Washington.

"In any sport, there are bound to be some rotten apples in the barrel as long as humans are involved," said Richard K. Lyon, a lawyer who has worked since 1975 to bring jai alai to the city. Lyon is a stockholder in one of the three groups that hopes to obtain a jai alai license if the referendum passes. "The law has a number of safeguards that would prevent corruption," he said.

Of all the forms of gambling that would be permitted if the referendum is approved, Washingtonians undoubtedly are least familiar with jai alai (pronounced hi-li or hi-ah-li).

The sport orginated in the Basque area of northern Spain and was introduced into this country as a betting sport in 1935. It is played in Connecticut, Rhode Island, Nevada and Florida.

Jai alai usually is played by two-man teams, whose players whip a small, hard, leather-covered ball around a three-wall court at speeds that sometimes reach 150 miles an hour. Usually eight teams play in each game.

If a player allows the ball to bounce twice or drops it from the long wicker basket tied to his hands, the other team scores a point. Seven points win the game. Bettors win money by picking the winner or the order of finish of the top three teams, similar to win-place-show selections in a horse racing bet.

The opportunity for large winnings -- a $2 bet can bring in $300 to $900 or more -- has generated enough interest in the somewhat exotic sport to attract as much as $60 million a year in bets at some jai alai arenas. And it is that potential for making money that has aroused some concern.

"The one thing you can predict when that much cash in involved is greed, and it's a hard game to regulate," said James E. Ritchie, former executive director of the federal Commission on the Review of the National Policy toward Gambling.

"The game involves skills we're not accustomed to monitoring in this country, and it's the only sport involving humans that we allow wagering on," said Ritchie, a lawyer who now represents Las Vegas casinos. "Basketball and baseball officials oppose [legal] gambling on their sports because of the pressure it would subject their players to."

In Connecticut, 11 bettors and players have been arrested on criminal game-fixing charges, and five of them have pleaded guilty. They have received suspended prison terms. Similar charges have been filed against many of the same people in Florida.

Connecticut gaming authorities also have fined the president and other officers and employes of World Jai Alai, Inc., of Miami $70,000 for failing to report allegations of game-fixing in Connecticut. The company, which operates six arenas, is one of the firms that has expressed an interest in operating in Washington.

According to testimony obtained so far in the criminal investigations, betters were paying players up to $150 a game to lose. In addition, some employes of the arena were receiving up to $200 a week to provide bettors with data on bets placed by others, so they could steer their bets to the highest-paying combinations.

Supporters of jai alai say the sport is not any more subject to fixing than other games.

"For the one scandal in jai alai there have been a whole bunch in horse racing and dog racing,' said Richard P. Donovan, president of World Jai Alai, Inc. of Miami.

Those who favor bringing jai alai to Washington say it would divert money from illegal gambling and lotteries in other states besides supplementing the District of Columbia's revenues.

"It's a good spectator sport. It's fast and has a good deal of grace and style and requires a lot of athletic ability," said Martin Firestone, a lawyer for Washington Jai Alai Inc., one of the groups that would compete for a jai alai franchise here.

"I think it's more exciting than tennis. It satisfies the human urge to wager on sports," said Firestone, who has worked on bringing jai alai to D.C. since 1975. In addition, he said, jai alai would be an "excellent tourist attraction. The District would get a percentage off the top and revenues through other taxes."

Three groups have indicated an interest in trying to obtain a franchise to operate a jai alai arena here if the referendum passes. To do so, they would have to be licensed by a five-member gaming commission established through the referendum. Usually, only one arena operates in a city.

Washington Jai Alai Inc., organized by Justin J. Schick, a retired Long Island, N.Y., jeweler living in Florida, played a crucial role in the gambling movement here, contributing one-third of the $22,000 paid persons to collect the 13,520 signatures that placed the gambling proposal on the ballot.

Schick has formed a business partnership with a broad-based group of well-connected Washingtonians. He owns 45 percent of the venture.

Some of Schick's newly-found associates are close to Mayor Marion Barry, who in the past has supported Legalized gambling but publicly has taken a neutral position on the referendum. They include Delano E. Lewis, an assistant vice president of C&P Telephone Co., who was the head of Barry's transition team, and Theodore Hagans, a prominent black developer who was chairman of Barry's inaugural committee.

Others are well-established in the city's civic and political hierarchy, including former Corporation Counsel Charles T. Duncan, realtor and businesswoman Flaxie M. Pinkett, Lyon Bryant G. Harris, an administrator at Howard University, funeral director R. Grayson McGuire and physician Edward Mazique.

Some have moved comfortably in the powerful circles of federal Washington, including lawyer tyler Abell, whose wife, Bess, is executive secretary to Joan Mondale, and Dale and Virginia (scooter) Miller, one-time intimates of President Johnson.

The biggest single personality in the jai alai movement here is Schick, who says he has spent $50,000 over the past five years in the hope of getting jai alai legalized in Washington.

"I'm no fool. You have a lot of visitors," Schick said during an interview in his home in Coral Springs, Fla. In Florida, tourists are one group that bet on jai alai often. Schick said he estimates his group would need $20 million to $25 million to carry out the venture. About $500,000 of that amount would have to be put up in cash. The source of the money is unclear.

Despite the tight money market, Schick said he expects most of the money to come from bank loans, even though the group's treasure, Abell, said no banks have yet been asked if they would put up the money for such an enterprise.

Schick said he plans to obtain his share of the needed $500,000 capital (about $250,000) by selling his house, now on the market for $99,500, and borrowing the rest from his family.

According to land records, Schick bought the four-bedroom house six years ago for $64,900 in cash. He said he obtained the money from the sale of his former home in Massapequa, N.Y. Land records there show Schick received only $19,500 in cash from that sale -- not $64,900.

"I paid the balance from my checking account," Schick said in a second explanation when asked about the discrepancy.

The second firm seeking to operate here is World Jai Alai, the company that was fined $70,000 by Connecticut authorities.

John B. Callahan, who served as the company's president until 1976, was described as "an associate of persons believed by the law inforcement community to be organized crime figures" in a 1978 report prepared by the Washington law firm of Wald, Harkrader & Ross for the Florida division of the Pari-Mutuel Wagering.

Asked for comment, Callahan replied, "that's bull . . ." and said his lawyer would call the reporter. No call was received from the lawyer.

Richard P. Donovan, the firm's current president, was a partner with Callahan in a Boston consulting firm. In an interview at World Jai Alai's Miami arena, Donovan said any suggestion of organized crime influence on the company was "preposterous."

"The management has never been implicated [in game-fixing] anywhere," he said. "To say you're going to have partimutuel betting without shady characters is like saying you're going to have politicians without graft."

The third firm seeking to operate here is Capital City Jai Alai Inc., organized by Louis Reyes, who owns two apartment houses in Washington. Investors with Reyes include Washington lawyer Arthur M. Reynolds, and Larry Brown, the former star running back for the Washington Redskins.

If the gambling measure is approved, the mayor, with the approval of the City Council, would select the five-member commission that would regulate gambling in the city.

The District of Columbia's proposed gambling law is modeled on measures now in effect in other states -- including Florida and Connecticut, where allegations of jai alai irregularities have occured.

Critics of jai alai said that these states have been lax in their regulation of the sport because strict enforcement would jeopardize the revenue it generated.

In Florida, for example, where 10 frontons gave the state $17 million in a recent playing season, the state had only two auditors with a $49 adding machine checking the results generated by the computers at the arenas, according to Dan J. Bradley, who, until last year, headed the state's Division of Pari-Mutuel Wagering.

Critics also say that jai alai is difficult to regulate because all of the critical elements that can be used to fix or otherwise alter the results of the game -- the players, computers, handicappers, and managers -- are controlled by management.

The industry itself is close-knit. Only seven companies own the 16 frontons in the United States. JAI ALAI IN WASHINGTON: Who Wants a Piece of the Action? The following persons are -- or plan to be -- investors in firms that say they will seek a license to operate jai alai arenas in Washington if the May 6 referendum is approved. WASHINGTON JAI ALAI, INC. JUSTIN J. SCHICK, retired Long Island jeweler now living in Coral Springs, Fla. TYLER ABEL, stepson of the late Drew Pearson. He is a Washington lawyer and the husband of Bess Abell, who is executive secretary to Joan Mondale. CHARLES T. DUNCAN, former D.C. corporation counsel and confidant of former mayor Walter E. Washington. THEODORE HAGANS, the only major black developer in Washington and the developer of the Fort Lincoln "New Town" and two proposed projects downtown. DELANO E. LEWIS, assistant vice president of C & P Telephone Co., on activist in many charitable and arts organizations and a confidant of Mayor Marion Barry. Lawyer Richard k. lyon and his wife Dorothy. He is former chairman of the Voice of Informed Community Expression, an influential civic group. Robert grayson mcGuire and his wife Elinor. He owns the McGuire Funeral Home, Inc. and is a former member of the D.C. Board of elections and Ethics.FLAXIE M. PINKETT, president of John R. Pinkett, Inc., a realiy firm. She is a long-time civic activist and a director of the National Bank of Washington. FLORA L. BRESS, the widow of David G. Bress, who was U.S. attorney for the District of Columbia. Lawyer Martin E. FIRESTONE and his wife Elaine. BRYANT G. HARRIS, one-time electrical contractor, former board member of the University of the District of Columbia and a coordinator for special projects at Howard University. Physician EDWARD MAZIQUE and his wife Frances who are prominent on the black social scene. Dale and virginia "SCOOTER" MILLER, once intimates of President Johnson. As a lobbyist, he has represented special interests from the state of Texas. Lawyer ROBERT R. SMILEY III and JOSEPH SMITH, a retired developer. CAPITAL CITY JAI ALAI, INC. LOUIS REYES, a real estate investor. LARRY BROWN, former Washington Redskins player and now a representative for E.F. Hutton & Co. Architect PAUL F. DEVROUAX, president of Devrouax & Purnell. JAMES A. CADE, assistance treasurer. Volpe Construction Co. Insurance broker HY FEINBERG. ROBERT H. SILBERG, an employe of Esquire Custom Tailors. Henry J. FERRAND, prpperty manager with J.C. Associates. ARTHUR M. REYNOLDS, a partner of criminal lawyer R. Kenneth Mundy who once represented former City Council Chairman Sterling Tucker. WORLD JAI ALAI, INC. ROGER M. WHEELER, chairman of Telex Corp., Tulsa, and his family.