The Supreme Court was asked yesterday to decide the constitutionality of a Tennessee law that allows police officers to "shoot to kill" fleeing suspects even when they are unarmed and the crime is nonviolent.

A U.S. appeals court overturned the law, saying it involved unreasonable and excessive use of force. The ruling came in a 1975 civil rights suit by a man whose 15-year-old son was shot in the head as he tried to flee an unoccupied house from which he had stolen two $5 bills and a ring.

Lawyers for the state and the Memphis Police Department argued that the appeals court decision placed an "undue burden on law enforcement." Henry Klein, attorney for the police department, argued that "determinations on when and when not to use deadly force should be left to legislatures, not to the courts."

About half of the states have laws similar to that in Tennessee. Many of the remaining states have more restrictive laws, generally allowing officers to shoot only when there is a danger to themselves or the public.

Steven Winter, an attorney for the boy's father, urged the court to uphold the appeals court decision and adopt the more restrictive standard. The state law and the Memphis police policy, he argued, "encouraged . . . excessive force."

Several of the justices appeared troubled by the case. Justice Lewis F. Powell Jr. asked Klein a series of questions about whether Tennessee's law made any distinction between violent and nonviolent felonies. Klein said that it did not and that shooting is justified if it is the only way to stop a suspect.

"Would you have the same [policy] with a fleeing felon whose felony was an antitrust violation?" Justice Harry A. Blackmun asked Klein. Klein said such a situation did not seem likely to occur, but, "Yes . . . the law makes no distinction between violent and nonviolent crimes."

Justice William H. Rehnquist asked Klein whether a policeman was not "obligated to shoot to wound" to stop a suspect and not necessarily obligated to shoot with intent to kill a suspect.

Klein said the police policy is to shoot for the "mass" or the torso, which is often fatal.

Chief Justice Warren E. Burger asked Winter several times what the officer should do if the facts were different and there were "two dead bodies in the house . . . . Would you still have a case?"

Winter said that his case would be more difficult but that the question would still be what the officer knew, not what he might have known. If the policeman saw an object in a suspect's hand that appeared to be a gun, Winter said, then the officer would have reason to shoot, even if the object turned out later to be something else.

Klein argued that police shooting a fleeing suspect could be justified in the case of a serious crime, and that burglary of a home is a serious crime that could become violent if a weapon were used.

"What do you suppose homeowners think about people who burglarize homes at night?" Justice Sandra Day O'Connor asked Winter.

Winter replied that people have a right to be concerned about being safe in their homes but that statistics indicate that violent burglaries are highly unusual.

A decision in the case is expected early next summer.