The District of Columbia auditor's office charged yesterday that the city's troubled Office of Human Rights is ineffective and "clearly" violates District law because the agency processes discrimination cases too slowly.

The highly critical auditor's report said that the human rights office takes an average of 279 days to determine whether there is merit to discrimination complaints when city law directs the agency to make such determinations within 120 days.

The report further charges that the human rights office is ineffective in several other ways and concludes that, as a result, District residents "are not adequately protected against discrimination."

The auditors found that Office of Human Rights investigators perform far below the average number of discrimination complaints that they could handle each month. The auditors also said in their report that the transfer of additional investigators from the federal Equal Employment Opportunity Commission to the city agency last fall had "no appreciable effect on the backlog of D.C. government cases.

The city auditors also questioned the quality of staff decisions in legal matters because many of the decisions were made by city human rights personnel "without any legal background or training."

The human rights office has been under fire from members of the City Council, which ordered the auditors to investigate the agency and issue a written report on their findings.

Council members have complained about the length of time it takes the agency to handle cases involving racial and sexual discrimination in public and private employment, public accommodations and housing.

The critical audit report comes at a time when the director of the Office of Human Rights, James W. Baldwin, is himself under fire for personal misconduct. Earlier this week, Baldwin admitted to the D.C. Board of Elections and Ethics that he violated the city's conflict-of-interest law by using D.C. government stationery to recruit students for a private university in Florida.

In addition, a member of Baldwin's staff complained last February that, despite the agency's heavy workload, the staff member was forced to prepare homework assignments that were a part of the work required for a doctorate degree in public administration that Baldwin later received from Nova University in Florida.

The staff member told reporters that the homework assignments were done during the regular work day when the Office of Human Rights employee was being paid by the city government.

At the same time as the homework assignments came to light, news reports alleged that Baldwin plagiarized substantial portions of his doctoral dissertation. A Nova University lawyer later recommended that Baldwin's degree be revoked because of this but the university has not yet acted on that recommendation.

In a letter sent to the City Council yesterday, Matthew S. Watson, D.C. auditor, said that "in light of the conflicts I see now, I believe that public hearings by the Council would be beneficial for a full airing of the (agency's) problems."

The City Council passed legislation last year to improve the effectiveness of human rights enforcement by detailing to the human rights office all equal employment opportunity officers from other D.C. agencies. Watson's report said the intent of that legislation was that the equal opportunity officers would be better able to enforce the law than Office of Human Rights personnel.

Baldwin responded to the auditor's report in a letter included as part of the report formally transmitted yesterday to the City Council.

The Office of Human Rights director criticized the audit, citing staff and budget reductions, an extraordinary workload of discrimination complaints and the lack of experience of the equal opportunity officers detailed to Baldwin's office last fall to help relieve the backlog.

". . . the Office (of Human Rights) has resolved more than twice as many D.C. government complaints in the past six months than were resolved during the first six months of 1976," Baldwin said.

"The audit report by Matthew S. Watson fails to identify the real problems in human rights enforcement," Baldwin said in his letter, "while attacking the efforts of a dedicated staff which has performed valiantly against odds few agencies have had to face."