Government-lotteries in 14 states have for the most part operated free of corruption, rigged games, major crimes and the influence of organized crime, according to law enforcement officials surveyed by The Washington Post.

Officials in Ohio, Pennsylvania and Connecticut conceded that they had some problems with rigged games. The worst was in Pennsylvania, where six people were indicted Thursday for allegedly fixing the daily drawing.

But these problems were apparently minimal. "We've had very, very minor problems," said Maj. Richard Campbell, head of the detective bureau of the New Hampshire state police, in a statement that was typical of those of law enforcement officials elsewhere. "We've had no problems. We're a small enough state so it can be policed well, and the profit goes to education.

District voters will decide next Tuesday whether to allow a lottery and daily numbers game here. The referendum they will vote on is a scaled-down version of one rejected last May largely because it would have also allowed betting on jai alai and dog racing.

The new proposal has nevertheless continued to draw sharp protest from some elements in the city, especially many ministers and politicians who rely heavily on churchgoers for support. But for the most part, strong opposition has waned, and most city observers expect the measure to be approved.

U.S. Attorney Charles F. C. Ruff, who opposed the May referendum in an extraordinary public statement, now says he has no problems with a legal lottery.

However some local law enforcement officials who are familiar with organized crime are apprehensive about legalized gambling. Proponents of legalized gambling are predicting that as much as $100 million might be bet in the District in the first year, and these officials say that is too great a temptation for organized crime to let pass.

Some officials believe a legalized lottery is just the first step to an open city, one where casino-type gambling which brings with it prostitution, loan sharking and certain organized crime involvement. "Once they get their foot in the door it's hard to stop them," said one law enforcement official. "They'll claim that $15 million from the lottery has been spent for kids, and that the same people who opposed the lottery were wrong and they are wrong to continue to oppose gambling."

However, the proposal on Tuesday's ballot would not legalize casino-type betting here or any forms of gambling except a lottery and daily numbers game for Washington, where many consider prostitution to already be usually open. Another law would have to be passed, either by referendum or by the City Council, to permit casino gambling.

Law enforcement officials interviewed in states where lotteries are allowed said they have not seen increased criminal activity with the advent of legal lotteries.

"I have been extremely impressed by our lottery operation; I have never heard or known of any transgressions whatsoever," said Lt. James Sharkey, commander of the major crime bureau of the Massachussetts State Police.

Law enforcement officials in New York, Maine, New Hampshire, Vermont, New Jersey, Maryland, Illinois, Maine, Rhode Island, Deleware and Michigan echoed these sentiments.

However, a law enforcement official in Connecticut, however, warned that these officials may be deluding themselves.

"A government starts a lottery believing there's a pie-in-the-sky and doesn't accept the fact that there may be a ripoff in it," said Austin McQuigan, chief state's attorney. "No state I know of has the resources to look into it."

In Connecticut, McQuain said, "I couldn't vouch for the integrity of the lottery yesterday, today or tomorrow. They could be picking our pockets and we wouldn't know it. We simply don't have any idea."

The state has had a special grand jury looking into possible lottery abuses, but the investigation has been piecemeal for lack of resources, he said. So far one state lottery official has been convicted for rigging a game. More people may be involved in such crimes, McQuigan said, "but we haven't pursued it simply because we don't have the money."

The worst lottery scandal to come to light has been in Pennsylvania, where a group connected to the state lottery has been indicted for rigging the daily drawing last April 24. One small group of gamblers won $1.2 million in one day.

That was the day the number 666 came up and the state had to pay out a record $4.6 million -- three times more than had been paid to play the game. A special grand jury found that some of the numbered balls had been weighted down with water, injected into them with a hypodermic needle. The balls numbered 4 and 6 had not been weighted down and thus popped up easier in the air-powered machine that selects the winning number.

Law enforcement officials in most states conceded that the existence of a legalized lottery has not affected illegal number betting. The District of Columbia has an illegal numbers game where an estimated $300 million is bet each year.

Many of these officials said a legal lottery actually boosts trade in the illegal games, because the media exposure gets people thinking about betting games.

"It's almost a form of free advertising for the illegal numbers," said Marilyn B. Peterson spokeman for the Pennsylvania Crime Commission. "They even use the state lottery winning number instead of coming up with one of their own. It's easier for them.

Other officials said bookies routinely lay off bets on the state lottery, that is, when customers bet heavily on one number, bookies will buy that number in the lottery to protect themselves in case the number wins. That is not illegal, but it helps such illegal operations, the officials said.