More than 1,000 District police officers yesterday pocketed overtime checks averaging $3,000 each, the result of a compensation lawsuit filed by the Fraternal Order of Police.

"It's a lot more than I expected," said Officer Cecil McNair, of the 5th District, holding a check for $4,206. "I thought I'd get a couple hundred dollars."

A federal judge ruled in favor of the union in January and ordered the city to pay the officers double their overtime salary -- three times their normal pay -- for overtime worked between April 15, 1986, and Oct. 1, 1987. About 1,300 officers shared in a total payout of $4.3 million.

Until October 1987, when the union negotiated its current overtime agreement with the city, the District government did not guarantee time-and-a-half pay for police officers who worked extra hours.

The union based its suit on a 1986 Supreme Court ruling that held that police officers are covered by the Fair Labor Standards Act, which guarantees time-and-a-half pay to private employees forced to work overtime.

After the January ruling in favor of the union, the city promised to give the officers their back pay by June or July. That deadline was later extended to October, the start of the new fiscal year, and then to November.

City payroll officials said the payments were held up because of the administrative burden of recertifying timesheets for so many officers and processing the new data.

"I cashed mine right away because I thought it might go bad," Byron T. Neal, a detective in the narcotics and special investigations unit, said with a grin.

Neal said his $1,825 in overtime compensation would go toward celebrating his retirement, scheduled for Dec. 29.

Robert Deso, a lawyer representing the union, said he petitioned the court last week to hold the District in contempt because of the delayed payments. His motion asked the judge to fine the city government $50 per day per officer if the payments were not issued promptly.

The checks issued this week went to plaintiffs in the largest of three overtime suits filed by the union. About 150 officers who sued the city in 1986 have received partial overtime compensation, and a few officers who filed suit last year are still waiting for a ruling.

Gary Hankins, head of the police union's labor committee, said the repeated delays in issuing checks damaged relations between city officials and police. "There's no question there's a lot of frustration," Hankins said. "We have very little faith in the city's word."

Not all police officers were happy about yesterday's overtime pay. Union offices on Fifth Street NW were deluged with telephone calls and visits from officers whose checks did not arrive or who had not participated in the suit.

"Why should you have to sue the government to get money you worked for?" asked LaVerne Epps, a 5th District officer. "They should be able to check payroll."

Hankins said the city had promised to issue checks to every plaintiff in the suit by today, and said the union will file another lawsuit in 1991 for officers who did not participate in the earlier ones.

The Supreme Court ruling that resulted in the payment prohibited the union from launching class-action suits, which would automatically include all eligible officers, Deso said.