The D.C. Court of Appeals yesterday ordered former D.C. City Council member Doughlas E. Moore to begin serving his long-delayed probation sentence for a 1976 assault conviction and chastized the city's Forensic Psychiatric Service for alleged political favoritism in its dealings with Moore.

Moore was convicted of assault for biting a tow truck driver in a 1975 scuffle in the City Council parking lot. He was sentenced in July, 1976, to pay a $500 fine and serve a six-month jail term, but the sentence was suspended and Moore was placed on two years' probation.

The probation conditions included requirements that Moore not violate any laws, regularly report to a probation officer and be examined by the court's forensic psychiatric unit.

However, Judge John W. Kern III said in a court opinion that the psychiatric unit apparently refused to carry out the judge's order to examine Moore because it "feared retaliation" since Moore was a council member at the time. The City Council approves the annual budget for the Department of Human Services, which operates the psychiatric unit. It is an agency that examines criminal defendants to determine their mental competency for Superior Court.

" . . . The law must be applied by those who work in and for the court system in all cases," Kern said, "Even in those that are politically sensitive. . . ."

Neither Moore nor his attorney, William A. Borders, could be reached for comment yesterday. Borders has argued that Moore did not violate the probation conditions because the court never had made arrangements for him to be tested by a psychiatrist. Kern's opinion, however, said that the "stark fact" remains that Moore had not complied with Judge Milton D. Korman's order.

Marjorie Henderson, the acting director of the court psychiatric unit, said the criticism was "unfair . . . We're just not in the business of refusing to do what a judge tells us to do."

Dr. David A. Lanham, who directed the unit when the incident involving Moore occurred, said that the decision not to examine Moore was based not on a fear of retaliation but on "conflict of interest."

"What if we had evaluated him and given him a clean bill of health psychologically? People might say . . . we were being intimidated because he was a public official."

Lanham said he recalled only one or two instances in which the agency had failed to examine a defendant because of a potential conflict of interest. The cases, he said, involved employes of the unit or the city social services agency.

Moore now much begin serving his probation period, and presumably undergo the psychiatric exam, according to the panel's opinion, which was joined by Judge Frank Q. Nebeker and concurred in by Judge Catherine B. Kelly.