The Supreme Court yesterday rejected a bid by an Alexandria woman to make the federal government pay damages for an illegal forced entry into her apartment. Heavily armed FBI agents and city detectives conducted the break-in, acting on a phony tip that newspaper heiress Patricia Hearst -- then a fugitive -- was inside.

The court's action reaches beyond the woman, Elizabeth Ann Norton, to hundreds and possibly thousands of innocent victims of illegal conduct by federal law enforcement agents.

At issue is the legal protection agents have if they acted in good faith in carrying out their official duties. If so the victims cannot successfully sue them, because the agents have a socalled qualified immunity, and the victims can not invoke the federal Tort Claims Act to seek damages from the government. In short, the victims have no remedy, unless Congress should amend the law.

That was the gist of a 2-to-1 decision made by the 4th U.S. Circuit Court of Appeals in July, when it reversed District Court Judge Robert R. Merhige Jr.'s order to the government to award her $12,500. Her only hope for collecting anything now appears to lie in a trial to determine if the FBI agents and detectives acted in good faith, as they claimed.

The agents and detectives went to Apt. 10 at 649 Notabene Dr. on the night of March 15, 1975, after an anonymous caller falsely claimed that Hearst was inside. They did not have a search warrant.

Not persuaded that the men at the door were FBI agents, Norton, then an employe of a Washington telephone answering service, refused to open it until they began to force it.

In an Alexandria trial before Merhige, experts supported her claim that the episode had inflicted serious psycological damage on her.

Merhige held that the entry violated Norton's constitutional rights. The only issue before the Supreme Court was whether the federal government was liable, and the court decided not to review the ruling.