A top Justice Department civil rights official hit a law school secretary in the head three years ago after an argument, then paid the woman's medical expenses in return for her agreement not to press criminal charges, according to the woman and school officials.

The official, Deputy Assistant Attorney General Robert J. D'Agostino, was at the time a law professor at Delaware Law School of Widener University in Wilmington. The school's dean at the time, Arthur A. Weeks, investigated the incident and determined that D'Agostino had no cause for hitting the woman, according to a letter Weeks wrote to the woman.

"I have told Professor D'Agostino that he did not have sufficient provocation to justify even the loud shouting at you much less striking you," Weeks wrote to Shirley M. Endicott. "In my reprimand I am emphasizing to him that it is expected that the faculty will set the tone for high professional conduct in this institution."

The 38-year-old D'Agostino, whose duties include reviewing civil rights laws involving sex discrimination, said in an interview yesterday that he hit Endicott in self-defense after she attacked him "fingernails first."

"I defensively swung my arms," D'Agostino said, striking Endicott "below the ear" with four fingers of his open hand. "I just don't duck. One should duck obviously when you have a woman going after you. You should duck but your reflexes are not to duck.

"I'm telling you I don't know for sure if she meant to rip my eyes out, her fingernails were in front of my face. When that happens suddenly, what do you do? If my reach were two inches less, I wouldn't come near her neck."

Endicott, now a secretary at Drexel University, said D'Agostino had asked her to type for him while she was typing for another professor. "I explained to him that I was in the midst of this job . . . . He continued to shout at me, and I said, 'With that attitude,' or words to that effect, 'I do refuse to do it.' I rippedit up and threw it into the corner. . . . He swung at me from across my desk . . . hit me, and knocked me against the file cabinet."

Weeks' letter to Endicott, who was 48 years old at the time, was verified for The Post by the present Delaware Law School dean, J. Kirkland Grant, who declined further comment.

D'Agostino later wrote Endicott expressing regret that the incident occurred, and paid her about $150 to cover her medical and legal expenses. He said yesterday that he did not consider that letter to be an apology, and denied that he had ever been reprimanded. Weeks, in an interview yesterday, said he could not recall whether he reprimanded D'Agostino and said he considered the incident "overblown."

A Justice Department official said yesterday that the department was unaware of the incident. Loren Smith, a member of President Reagan's transition team and also a Delaware law professor, said that he knew of the incident when he recommended D'Agostino for the job and considered it insignificant.