In November 1979, the D.C. Department of Human Services received a tip that a 24-year-old woman with three children had illegally received public assistance for nearly a year by hiding the fact that her husband was employed and living at home.

What's more, the couple had recently moved from Washington to a $21,500 house they bought in Prince George's County. Yet they continued to receive welfare checks that the city unwittingly mailed to a relative of the couple who lived in the District of Columbia.

The woman was dropped from the welfare rolls. But four months later, in March 1980, she reapplied to DHS for assistance and immediately began receiving $476 a month in Aid to Families with Dependent Children AFDC and food stamps.

In all, the woman received $10,746 in questionable welfare payments before she was dropped from the rolls a second time, in September 1980, according to DHS records. One of her husband's coworkers tipped off DHS to the ruse.

The woman's case in many ways typifies the problems of deceit by welfare recipients and administrative bungling that have plagued the city's AFDC program in the past and contributed to an estimated $50.8 million in "overpayments" to ineligible recipients between 1978 and 1980.

In the past, the woman's case probably would have received scant attention from city prosecutors, who placed a low priority on welfare-fraud cases, or from DHS officials who were reluctant to force destitute families to repay the government.

But under intense pressure from Congress and the Reagan administration, the D.C. government has begun to crack down on welfare fraud and recently adopted tough new federal guidelines for determining recipients' eligibility and for recovering illegal payments.

Since February, the D.C. corporation counsel's office has started investigations into 23 cases of suspected welfare fraud involving about $128,000 in overpayments.

Three of the suspects -- Bessie McDuffie, 39; Rosita Carmen, 34, and Theresa Scott, 27 -- pleaded guilty last spring to misdemeanor welfare fraud charges in D.C. Superior Court. All three admitted to illegally collecting D.C. welfare payments while living in Maryland.

McDuffie, the mother of four children and a supervisor of maids at the Mayflower Hotel, illegally obtained $30,000 in welfare payments over a 10-year period to improve her middle-class standard of living, according to prosecutors.

McDuffie and her husband, who also is employed, live together in a $72,000 house in Clinton and own three cars. To trick DHS, McDuffie rented a city public housing unit and used it as a mail drop to collect her AFDC checks. She was sentenced in June to spend 26 weekends in jail and to make restitution.

Carmen, the mother of three children, was convicted in May of illegally obtaining $10,000 in AFDC payments between 1972 and 1976 by using her sister's D.C. address as a mail drop. During that time, Carmen lived in Laurel with her husband, who held a job. She awaits sentencing.

Scott, an $11,000-a-year clerk typist with the Department of Labor and the mother of two, moved from Washington to Oxon Hill in 1979 without telling DHS. She was convicted in May of illegally obtaining $5,000 in welfare payments. She received a two-year suspended sentence and was ordered to repay the money.

While these amounts are substantial, they still pale by comparison with the celebrated 1977 case of Linda Taylor, a Chicago woman known as the Welfare Queen. She was convicted of illegally receiving welfare checks that the government said amounted to more than $150,000 a year.

One of the D.C. cases still pending involves a woman who worked for the District while illegally receiving AFDC payments, according to a source. Another case involves a Maryland woman who held a low-paying job in a Senate office building while collecting D.C. welfare benefits, the source said.

Three of the cases, including that of the Prince George's County mother of three, were referred to the U.S. Attorney's office for possible action. The D.C. corporation counsel lacked authority to issue misdemeanor arrest warrants for those suspects because they live outside the District.

One city prosecutor acknowledged recently that the city's crackdown on welfare fraud was spurred by a General Accounting Office GAO investigation of the city's AFDC program, which began late last year.

In a report released last month, the GAO charged that the D.C. government's laxity in recovering overpayments and prosecuting ineligible recipients contributed to an error rate in AFDC payments ranging from 32 percent in 1978 to 11 percent this year. Washington's current error rate, while vastly improved, still exceeds the national average of 8.3 percent and is nearly triple the 4 percent limit set by the federal government. States that exceed that limit next year may face the loss of federal matching funds.

The GAO study also criticized the D.C. corporation counsel for failing to prosecute a single welfare fraud case between 1978 and 1980, despite receiving an average of 500 leads a month from DHS officials on cases of potential wrongdoing.

The GAO's findings angered city prosecutors, who insisted that most of the DHS' "leads" merely consisted of lists of suspects and the amounts of money involved, but none of the documentation essential to proving a case in court.

"Cases simply were not presented to us in a realistic form that you could make prosecution judgments on," said Geoffrey M. Alprin, deputy corporation counsel for the criminal division.

"We probably could have taken the initiative earlier to encourage DHS to provide better cases ," Alprin conceded. "We could have done more, but it would have meant doing less in other areas."

Before the city's new get-tough policy, Alprin's office devoted most of its energies to prosecuting traffic cases, violations of housing and zoning codes, illegal disposal of waste and juvenile court cases.

City prosecutors spent little time on welfare fraud cases because they were hard to prove, DHS records often were vague or incomplete, the amounts of money in dispute often seemed inconsequential and juries were reluctant to convict women struggling to feed and clothe their children.

"It's tough to get our line attorneys enthusiastic about going after some welfare mother over $2,000," Alprin said. "That's very tough."

However, a veteran DHS analyst, who asked that he not be named, contends that political forces discouraged city employes from being more aggressive in reducing the AFDC error rate and combating welfare fraud.

"The general philosophy was not to get the error rate down," the analyst said. "It was a political issue. Why do you want to screw up your constituency? Ineligibile recipients vote, too."

DHS routinely verifies information supplied by about a third of the AFDC recipients. Those families either receive some outside income or are considered prone to error in filling out their applications for welfare. The remainder are subject to random checks.

DHS verification checks often include comparing the names of D.C. recipients to names appearing on the welfare and unemployment rolls of neighboring states.

DHS officials said recently that many of the past problems with the AFDC program stemmed from an antiquated record-keeping system and a shortage of employes to process applications and review clients' eligibility. Part of that problem was alleviated in 1978 when Congress authorized DHS to hire 180 additional employes to handle the AFDC caseload, according to an official.

Under new procedures, tentatively approved last week by the D.C. City Council, AFDC clients for the first time must file monthly statements with DHS outlining their financial status and family situation.

DHS will be required to recertify the 28,000 families on AFDC every six months to weed out ineligible recipients. The GAO report said that the city's AFDC error rate could have been substantially reduced in the past if DHS had adhered to that procedure. However, DHS is seeking a federal waiver to limit recertification to once a year.

DHS also will be required under the new rules to take "all reasonable steps" to promptly recover AFDC overpayments, provided such action doesn't cause extreme hardship for the recipients.

DHS has begun to switch to a computerized processing and record-keeping system that officials claim will make it easier to determine eligibility and to check up on current and former welfare recipients.

The old filing system was cumbersome and time-consuming to use, officials said. Welfare workers occasionally didn't bother to check the central files to determine whether an applicant had received payments in the past.

It may have been an administrative mistake of that sort that enabled the Prince George's County woman to slip back on the welfare rolls, according to Alice Ricci, the DHS's acting deputy administrator for income maintenance administration.

"It was a manual system and that possibly could happen if the original case was not retrieved," Ricci said. "It is possible they could have come back in and the worker did not know. But from now on, with the computer system, those kinds of cases will be flagged."