Dr. Robert J. Sherman, who was accused of performing an incomplete abortion on a 16-year-old patient that led to her death, pleaded guilty in D.C. Superior Court yesterday to 25 counts of perjury in exchange for the government's dismissal of a second-degree murder charge against him.

Sherman, 66, who appeared calm as he sat in a courtroom crowded with spectators, faces a maximum penalty of 10 years in prison on each of the 25 perjury charges. He is scheduled to be sentenced by Judge Fred B. Ugast on May 31.

The plea bargain agreement, worked out by Sherman's defense lawyers and the U.S. Attorney's Office, was made final yesterday.

Sherman, who ran an abortion clinic at 1835 I St. NW, was indicted on murder charges a year ago in connection with the 1975 death of Rita McDowell. The indictment also charged that Sherman lied to a grand jury, to a medical licensing board and in civil lawsuits in an effort to cover up the circumstances of McDowell's death. In addition, the grand jury said. Sherman induced employes to lie for him about conditions at his abortion clinic.

Sherman's trial on the murder and perjury charges began last October, but after eight weeks of testimony the case finally ended in a mistrial.

Principal Assistant U.S. Attorney Carl S. Rauh said in a statement presented in court yesterday that the government agreed to drop the murder charge and accept Sherman's plea of guilty to the 25 perjury counts at the request of the dead girl's mother, Lupe McDowell.

"Since the death of her daughter more than four years ago, Mrs. McDowell has testified in four separate, lengthy proceedings concerning the circumstances surrounding that tragic event," Rauh said. "In each of her appearances, Mrs. McDowell has had to relive the death of her daughter. . . It was her very strong preference not to undergo the anguish of another lengthy trial."

Rauh said the government also felt that guilty pleas entered by Sherman "obviously exposes the defendant to the possibility of a lengthy period of incarceration."

"We believe it is in the public interest that there be finality to the Dr. Sherman case and the litigation surrounding the death of Rita McDowell. . .," Rauh said. "Going through another lengthy trial at a great cost to the community would not effect a significant difference in terms of the ultimate sentence the defendant would be exposed to."

Robert F. Muse, of the city's Public Defender Service, who represented Sherman with attorney Constance O'Bryant, said in a brief statement that the government's reasons for entering into the plea bargain arrangement "are not completely shared by Dr. Sherman."

"For nearly four years, my client has been living a virtual nightmare," Muse told Judge Ugast. "He sought this agreement because he wanted to bring his life back to some sense of reality."

"What my client has admitted today is that he lied on several occasions," Muse said. "But I'm sure if all of us look deep inside of ourselves, we'll find that we've also lied at some point in our lives."

Muse emphasized that Dr. Sherman's pleas of guilty to perjury "were not tantamount to an admission of guilty" to the murder charge.

During Sherman's trial, the defense argued that McDowell died as a result of the grossly negligent treatment she received at D.C. General Hospital. McDowell died in the Hospital's intensive care unit four days after she went to Sherman's clinic for an abortion.

Sherman's lawyers presented no evidence during the trial in defense of the perjury charges brought by the government.

Rauh, and Assistant U.S. Attorney Whitney S. Adams, contended that Sherman deliberately performed incomplete abortions and routinely violated medical standards in order to cut costs and increase profits at his clinic.

Expert witnesses for the government testified that McDowell's death was the result of blood poisoning and shock that followed an incomplete abortion.

The trial itself was plagued with problems, including charges that defense witnesses were harassed and Sherman's own illness just as the case was about to go to the jury for deliberation.

At one point, a female juror was dismissed from the case after she suddenly disclosed that she knew a former patient of Sherman's who was about to testify for the government. It was another juror's allegations that she had received threatening telephone calls about the case that eventually led Ugast to declare a mistrial.

Following the juror's disclosure, Ugast privately questioned each member of the jury. Delays caused by that questioning, and concern that the privacy of the jury may have been violated, led him to declare the mistrial, Ugast said.

Sherman's license to practice medicine in the District was revoked in September 1977. CAPTION: Picture, Dr. Robert Sherman, right, leaves courthouse with lawyer. By Fred Sweets-The Washington Post