The D.C. Department of Human Resources will begin a new screening program next week to reduce overpayments to welfare recipients and remove ineligible families from the city's relief rolls, Mayor Walter E. Washington announced yesterday.

Recently, 22.4 per cent of the recipients in the city's program of Aid to Families with Department Children were found to be getting overpayments, according to acting DHR director Albert P. Russo, and 13.2 per cent were determined to be ineligible. "There's no question about the fact that the error rate is intolerably high," said Russo, seated beside the mayor at a news conference.

The city's goal, Russo added, is to reduce the ineligibility rate in the AFDC program to 3 per cent and the overpayment rate to 5 per cent. These are levels set by the U.S. Department of Health, Education and Welfare, which pays half the cost of the city's AFDC program.

In another development, the mayor announced that the city had filed an affidavit in U.S. District Court, contending that DHR now is in full compliance with a court order requiring speddier handling of welfare applications. Earlier this month, the mayor said the city had fulfilled part of the court order by catching up on a backlog of 899 applications.

In the newly-submitted affidavit, filed Monday afternoon, the city said that no further backlog has developed, that every application now is being accepted on the same day an applicant tries to submit one, and that applicants are being given both oral and written notice of their legal rights The District of Columbia government "is in full compliance with the mandates of law and the court's order, and I shall strive to see that it continues to remain in compliance," Russo said in the affidavit.

The city's actions in the 3-year-old court case represented its response to an order by Judge Aubrey E. Robinson Jr., who has already ruled five D.C. officials, including the mayor, in contempt of court for failing to comply with an earlier order.

Gerald W. VonKorff, a Neighborhood Legal Service Program lawyer representing plaintiffs in the case, said yesterday that he had not yet received a copy of the xity's affidavit and was uncertain whether he would file a reply to it. "That's good, if that's true," he said of the city's assered compliance.

The city's program for uncovering overpayments and ineligibility among AFDC recipients was described by city officials yesterday as a sophisticated, computerized system designed to screen out cases that are, theoretically at least, most likely to show some irregularity. Such cases would be reviewed by a special, centralized staff of 62 welfare workers to determine whether any improper welfare aid has, in fact, been provided.

The system was devised jointly by DHR officials and the General Accounting Office, Congress' auditing arm. Officials said yesterday that eight of 10 criteria would be used to screen out AFDC cases for special review, but they refused to name most of them, arguing that disclosure could impair the screening program's effectiveness. The only criterion cited at yesterday's news conference was earned income.

The city's AFDC program - which, according to Russo, now provides aid to 107,000 D.C. residents - has repeatedly has drawn criticism. GAO told a Senate subcommittee last September that the District erroneously had paid $26.6 million to welfare recipients who "willfully misrepresented their eligibility" from 1971 to 1975.

Rep. William H. Natcher (D-Ky.), chairman of the House D.C. Appropriations Subcommittee, raised the issue Monday during hearings on the city's budget. "Would it be correct to say that there is no system in the District to take ineligibles off the rolls?" Natcher asked Ulysses Banks, a D.C. welfare Official. "Sad as it is, it's correct," Banks replied.