A citizens commission formally recommended yesterday that several forms of gambling be legalized in Washington, including creation of a city lottery that could bring the District government as much as $37 million a year in new revenue.

The commission urged that parimutuel betting be permitted here on races run in other states. It also proposed that churches and schools be permitted to run bingo games and raffles. And it called for the lifting of laws against social gambling in homes and public places.

THe commission report, which calls for a citizens vote to determine whether they want a lottery, was presented by its chairman, Brant Coopersmith, to the D.C. City Council.

Maryland and numerous other states have lotteries of the type proposed for the District. New York has a state-owned corporation that accepts off-tracks bets on horse races.

Horses racing and on-track betting are legal in Maryland. Virginia's General Assembly has authorized a referendum on legalizing par-mutuel betting in the state.

A report last year showed 13 states operating lotteries that grossed $1.1 billion, paying a large portion of that sum in prizes. COnnecticut reported a lottery profit of $22 million. New York state took in $24 million from off-track betting.

No early action by the council on the commission's recommendations is expected. Even Councilman Marion S. Barry Jr. (D-At Large), the sponsor of the resolution adopted in 1976 that created the commission, said the report "must be examined thoroughly before any action can be taken."

Existing laws, passed by Congress, prohibit gambling in the District. However, the D.C. City Council is scheduled to assume the power to change those laws next January.

The gambling proposals seem likely to figure prominently and controversially in this year's mayoral and coucil election campaigns. They already are opposed by many of the city's most prominent and politically active Protestant clergymen, notably Baptists.

Barry and Council Chairman Sterling Tucker, both announced mayoral candidates, said they would support the advisory referendum but were silent on the other proposals.

A spokesman for Mayor Walter E. Washington, an unannounced but probable candidate for reelection, said the mayor remains opposed to most forms of gambling, but wants to read the report before commenting.

On its key vote, take last November, the citizens commission voted, 19 to 3, to support a city-run lottery including a daily numbers game. Chairman Coopersmith said most other recommendations were approved by slightly narrower but still-decisive margins.

"There is little doubt as to where the people in the District of Columbia stand" on the issue, said Coopersmith, who is Washington director for the American Jewish Committee. "Approximately 80 percent of the population want it," he said, citing media polls on the subject.

Other than estimating the profit from a city-operated lottery at between $16 million and $37 million a year, the report did not project a tax yield from all the forms of legalized gambling that it recommened.

The profit estimate is based on the city's keeping 40 percent of the money collected from lottery ticket sales and paying out 60 percent as prized to winners.

The commission recommended that the profits be put into a special fund, separate from the city's operating treasury, and be used to finance social and educational services and city-operated programs for which funds are not currently appropriated.

It proposed the creation of a five-member D.C. Gaming Control Board with the power to regulate all legalized gambling.

Coopersmith said the commission considered but decided not to recommend two forms of gambling - casino gambling, such as that in Nevada and recently legalized in Atlantic City, N.J., and betting on such sports events as football and basketball games.

The report contained two minority reports, one advocating a higher payout of prizes in the lottery and the second broadly attacking the legalization proposal on economic and social grounds.

Three clergymen on the commission - the Revs. John D. Bussey, Reginald Green and William A. Treadwell - were joined in the second dissent by Anita Shelton, whose chief concern was the economic impact on low-income people.

"Gambling does not lend itself to regulation," their minority report asserted. ". . . A government could just as easily justify itself in 'regulating' burglary, larceny, flimflam, prostitution and even murder . . . Gambling, ultimately and eventually, leads to all these things."