Sterling Tucker was running late for another mayoral candidates' debate. So when he walked into the parish hall of a southeast Washington church one recent evening he strode briskly to the front of the room.

What he heard as he walked down the aisle at the Ryland Epworth United Methodist Church made even Tucker smile, however fanitly. Almost on a cue to Tucker's entrance, Dorothy Maultsby, another candidate in the District's Sept. 12 Democratic mayoral primary, was telling the crowd that if she is elected mayor she would make certain the city's CETA money is properly used.

As many people in the audience of 125 laughed at the timing of Maultsby's remark. City Council Chairman Tucker realized that, like a recurring bad dream, the CETA issue just won't go away.

When it was his turn to speak, Tucker devoted the first half of his allotted five minutes talking about CETA.

Tucker has been questioned and criticized on the CETA issue ever since July 17, the day the Department of Labor charged that the City Council's participation in the federal government's Comprehensive Employment and Training Act program was riddled with favoritism and abuse.

While Tucker has denied any wrongdoing, he has acted swiftly to try to reduce the political fallout of the issue. He led a move to draft a new set of rules for the hiring and assignment of council employes who are paid under the CETA program. Tucker also beat Mayor Walter E. Washington, one of his chief mayoral opponents, to the punch in sending a letter to the city's congressional budget overseers asking that the city be allowed to work out its own CETA guidelines and not have stricter restraints imposed on it and those in other cities.

Tucker campaign aides say that their continuing canvassing indicates that Tucker is not being hurt politically by the flap over CETA, but Tucker concedes that "it's negative to the extent that it's not a plus.

'I'm assuming the leadership in cleaning up whatever problems there might be, to put the program beyond the pale of a question of how people get hired," Tucker said. "How I handle it is what people ought to be looking at."

CETA is designed to provide work and job training for unemployed and disadvantaged people. The Labor Department said that in the District a few relatives and friends of council members got jobs. One of Tucker's CETA workers cited by Labor was Lorethea Davis, the wife of a dentist who is Tucker's campaign treasurer. In all, Labor said it found at least 78 instances in which the hiring of past or present CETA-paid council employes violated government guidelines or lacked written justification.

As chairman of the council, it is Tucker who is continually asked at candidate forums about CETA, even though one of his key opponents, Marion Barry, is on the City Council, and another, Washington, as mayor, has the ultimate responsiblity for the city's CETA program. In the year ending Sept. 30, more than 23,000 people in the District will have been given jobs or trained with $48.1 million in CETA money.

District officials are currently working on a report, due by Aug. 17 to explain to the Department of Labor the hiring of the 78 workers in question.

Tucker and other city officials say they will dispute some of Labor's findings and justify others.

At one candiate forum, Tucker told a questioner: "Let me say this, I know of nobody presently on CETA payroll working for the council staff who ought not to be there . . . no one who is not qualifed to be there, who has not met the requirements. The problem is that the Labor Department guidelines are not clear.

He said that Davis qualified for her job because she had been unemployed for the 30 days before she began working for the council. Moreover, Tucker said in an interview that Davis applied through normal employment channels and that he has picked no one for CETA-paid council jobs.

Tucker said the problem in the CETA requirements dictating any family income limit above which unemployed members of a family could not be hired under CETA.

"I don't know what their financial requirements are," Tucker said of the Davises. Lorethea Davis and her husband Howard, a vice president of the Independence Federal Savings and Loan Association, live in a house over-looking Rock Creek Park that is worth well over $100,000 and three years ago took out a second mortgage on the house for $130,000.

Maultsby and John L. Ray, two Democratic mayoral candidates not now in the city government, have wasted few opportunities to castigate Tucker, Washington and Barry about CETA and other alleged shortcomings in the District Building.

"We have to begin to be responsible for some moral standards in recruiting," Maultsby said in an interview. "Whereas the guidelines might allow (Davis' hiring), we have to look for those who most need work. I think Sterling Tucker was absolutely wrong."

Ray tells voters that the District's operation of CETA is "an example of petty corruption that is causing the city's people to suffer while (D.C.) officials take care of their friends and political cronies.

"When you look at the D.C. government," Ray says, "the buddy system "runs throughout. We need a clean sweep."

"I don't blame the opponents who are on the outside for wanting to make an issue of it," Tucker said. But he steadfastly defends the council's CETA hiring record and notes that the Labor Department reviewed the program a year ago and made no recommendations for any changes in hiring procedures.

"If there are problems," Tucker said, "I want to acknowledge them and correct them."