The director of the federal office investigating auto defects was engaged to the secretary of a top General Motors Corp. vehicle safety executive while he was supervising a probe of potentially deadly brake problems in GM's X-body cars, General Accounting Office auditors have discovered.

GAO officials notified the National Highway Traffic Safety Administration recently that the relationship gave "the appearance of a conflict of interest" in the government's handling of the defects case.

But an internal memo written by NHTSA chief counsel Frank Berndt says George Anikis, former director of the Office of Defects Investigations in the NHTSA, advised his superiors about his relationship with the woman who now is his wife, "and did in fact seek relief from the dilemma" presented by the conflict between his personal life and professional obligations. Anikis is not guilty of "a meaningful violation" of federal conflict-of-interest laws, the Berndt memo concluded.

Anikis himself notified NHTSA officials that his fiancee owned $35,000 worth of General Motors' stock and asked to be transferred off the GM case, NHTSA sources said.

NHTSA officials did not immediately remove Anikis from the GM investigation after learning of his relationship with the GM employe, according to GAO documents, which were leaked yesterday by private critics of the agency.

The documents say GAO is also investigating whether Anikis traveled to Detroit at government expense to meet with his fiancee when she was working as a $25,000-a-year secretary in the Office of the Director of Product Investigations on the GM engineering staff.

The matter reportedly is not mentioned in a GAO report on NHTSA's handling of the X-car brake defect, which is scheduled to be discussed at a congressional hearing today.

On Wednesday, after a four-year investigation of defects in X-car brakes, NHTSA filed an unprecedented $4 million suit accusing GM of endangering its customers by trying to cover up braking defects in its 1980-model X-body cars.

On the day the lawsuit was announced, NHTSA itself was accused of engaging in a cover-up by concealing alleged improprieties in its handling of the braking case. Those charges were brought by Rep. Timothy E. Wirth (D-Colo.), chairman of a House subcommittee that oversees NHTSA, which is holding hearings on the matter today. GM was invited to testify but declined yesterday.

"We are deeply concerned, once again, over the lack of basic fairness. The reputation of GM cars and the interests of the people who make them have become a pawn in a conflict between units of two different branches of government," GM Vice President for Public Affairs Elmer W. Johnson said yesterday.

The "conflict" Johnson alluded to is the long-running battle between Wirth and NHTSA. For nearly a year, Wirth has been accusing the agency of laxity in enforcing automotive safety.

Wirth asked for a GAO investigation of NHTSA and plans to release preliminary results of the seven-month study today. GM and congressional sources charge that NHTSA's primary reason for suing the company was to reduce the impact of the GAO report.

NHTSA officials deny that allegation and retort that Wirth is spearheading a Democratic attack on the agency for political reasons. They contend the distribution of internal documents on Anikis is an example of politically motivated attacks on the agency.

Anikis said he has been ordered by NHTSA officials not to discuss the allegations. Agency officials also refused to comment.

Anikis, 49, the divorced father of five teen-agers of whom he has custody, has told acquaintances that he met his current wife, Anne, 41, in the summer of 1981. She was then a secretary for GM's director of product investigations--which deals directly with NHTSA matters.

Anikis' colleagues say he insists he told his superiors about his relationship and tried for six months before his marriage in October 1982, to find another job in the government.

"His wife had been at GM for 21 years. She was moving from her hometown in Detroit to start life with a whole new family. She was selling her house. They George and Anne figured she could get a job with GM in the Washingon area. He was ready to give up his job because she already was giving up so much," one source said.

Anikis was transferred to an NHTSA office dealing with alcohol programs three weeks after his marriage. His wife decided against seeking a Washington job with GM because of possible conflicts of interest, associates say, and took a lower paying job with another company.