A D.C. Superior Court judge yesterday appointed lawyers from the city's Public Defender Service to represent former Washington abortionist, Dr. Robert J. Sherman, at his trial on second-degree murder and perjury charges.

Sherman told Judge Alfred Burka yesterday that his sole income is a $63-a-month government pension, that he lives in an apartment furnished with a bed and bureau from the Salvation Army and Good will and that he has not paid "one penny" to the lawyer he had hired to defend him against the charges.

"I am broke, b-r-o-k-e," Sherman told Burka yesterday.

Sherman fired his attorney, John W. Karr, on Wednesday. A court official later determined that Sherman , now lives in Richmond was indigent and eligible to have a lawyer appointed and paid by the court.

Sherman was scheduled to stand trial in Superior Court on Tuesday. He is charged with second-degree murder in connection with the death of 16-year-old Rita McDowell after an incomplete abortion performed on her three years ago. He is also charged with 17 counts of perjury and nine counts of inducing some of the former employes at his abortion clinic to lie for him about procedures there.

Principal Assistant U.S. Attorney Carl S. Rauh told Burka yesterday that Sherman's sudden announcement that he could not afford a lawyer is "nothing but an effort by Dr. Sherman to delay this matter so that he doesn't have to face trial."

When he was indicted in April, Sherman was employed by the city of Richmond's health department and maintained a general medicine and gynecology practice in a Richmond suburb.

Under questioning by Rauh yesterday, however, Sherman said he was fired from his city job following publicity about the indictment. His private practice, Sherman said, is now "practically shut down." He said he has two to five patients whom he sees "once in a while", and makes an occasional house call or telephone call related to his practice, but that his fees go to laboratory and office costs.

What money is left, Sherman testified, "is enough to buy some food, that's all."

When asked by Rauh about his ownership in 1974 and 1975 of more than $250,000 worth of stock, Sherman said the assets had been sold to pay defense lawyers in connection with civil suits brought against him.

"It's all gone," Sherman said.

In October 1976, Sherman settled a civil lawsuit brought by Rita McDowell's mother by agreeing to pay the family $525,000.

Sherman's license to practice medicine in the District was revoked a year ago. Since then, Sherman asserted, he has briefly held jobs in Maryland and Virginia, where he is licensed, but was dismissed because of adverse publicity.

He told Rauh he now has less than $100 in two accounts and that the rent on his Richmond apartment has been paid for the past three months by his sister.

At the close of yesterday's hearing, Burka agreed to provide Sherman with free lawyers from the Public Defender Service, which takes selected, serious cases on behalf of indigent defendants.

Burka also appointed Karr to assist the public defender in preparation of the case for trial. Karr will be paid with court funds, Burka said. A hearing on the status of the case will be held on Wednesday.