The D.C. government paid out $50.8 million in welfare benefits to ineligible recipients between 1978 and 1980, but recovered only $140,000 of those funds, according to a study prepared by the General Accounting Office.

During that period, the D.C. corporation counsel received an average of 500 leads a month from city welfare officials on cases of potential welfare fraud, but not a single case was prosecuted, the report stated.

The GAO concluded that the D.C. government's laxity in recovering overpayments and prosecuting ineligible welfare recipients contributed to payment error rates ranging from 32 percent in 1978 to 11 percent this year.

The current D.C. error rate is nearly triple the 4 percent limit allowed by the federal government without penalty of a possible loss of federal funds, and it exceeds the national average of 8.3 percent.

"Strong collection efforts reduce error rates by serving as a deterrent to people who might otherwise try to obtain benefits to which they are not entitled," the GAO report said.

D.C. Human Services Director James Buford said yesterday, "I think that the error rate has been tremendously reduced over the last three years. We have a lot of work to do to meet the 4 percent rate. We think the activities now under way . . . should enable us to achieve the federal goal."

The U.S. Department of Health and Human Services has ordered all states and the District of Columbia to reduce error rates in the Aid to Families with Dependent Children program to 4 percent by Sept. 30, 1982, or risk losing federal matching funds for payments made above the 4-percent target.

The federal government contributes half of the money spent annually on AFDC recipients in Washington, where the current AFDC budget is $94 million, according to a DHS official.

In New York City, where the payment error rate is 9.7 percent, welfare agency officials were warned this week that they may be penalized tens of millions of dollars unless they met the federal target.

However, city officials there indicated that it might be easier and less expensive to suffer the penalty than to correct the mistakes.

Buford said yesterday he expects his department to meet the federal guideline by following new reporting requirements and implementing a computerized system for determining recipient eligibility.

In the past, Buford's department failed to review AFDC cases every six months, as was required by federal law, to see whether clients were still entitled to benefits.

Under new D.C. and federal policies, roughly a third of the 29,000 families receiving AFDC must be recertified every three months. Also, recipients must make monthly reports to DHS on their employment status, income and dependents.

City Administrator Elijah B. Rogers had urged the GAO to delay releasing its report until the federal agency had a chance to evaluate the impact of the new D.C. and federal reporting policies.

In a letter to the GAO, the investigatory arm of Congress, Rogers said the city intends to "pursue overpayments more vigorously," but would not "attempt recoveries that are not cost-effective or . . . prosecute potential fraud cases in which the evidence is ambiguous or the amount trivial."

Last February, several months after the GAO began its study, the corporation counsel's office began investigating 10 cases of suspected welfare fraud. Three of those investigations led to convictions.

"We believe this limited resumption of case referrals and its initial success demonstrate the value of such practices," the GAO said. "While it is unreasonable to expect that most of the 500 to 600 potential fraud cases each month would be prosecutable, it is also unreasonable to expect that the number of cases would dwindle to only 10 per year."

Until now, city lawyers have been reluctant to prosecute welfare fraud cases because they are difficult to prove, and because the lawyers think there are more important matters to pursue, such as violations of zoning and fire codes and traffic laws.

AFDC overpayments usually are caused by DHS administrative errors, misundertandings between DHS employes and welfare recipients, or willful deception by recipients, according to the GAO study.

DHS usually seeks restitution only in cases where the recipient had provided incorrect eligibility information. Even then, the department cannot get its money back unless the client voluntarily signs a restitution agreement.

DHS employes told the GAO they were reluctant to add to the economic hardship of families on AFDC by demanding repayment.

Also, recipients often insist that they reported changes in their circumstances, but that their case workers neglected to record them.

"Statements like these are difficult to disprove in court, and judges and juries are often sympathetic to the plight of these individuals," the GAO report stated.

In a few instances, the corporation counsel's office concluded that the dollar value of an alleged fraud was high enough and there was sufficient evidence to refer the case to the U.S. attorney's office for possible prosecution as a felony. Since 1978, about five to 10 such cases were referred to the U.S. attorney every year, but none was prosecuted.