The Supreme Court yesterday let stand a lower-court ruling that the federal government could not be held liable for the deaths and injuries allegedly caused by above-ground atomic bomb testing in Nevada in the 1950s.

The justices, without comment, said they would not hear an appeal by about 1,200 people who either lived downwind from the nuclear test site or who represented alleged victims of low-level radiation exposure from fallout during the testing.

The 1979 lawsuit, Allen v. U.S., argued that the federal government was negligent in monitoring testing results, and in failing to warn people of the danger they faced from radiation or telling them how they could protect themselves.

A federal judge ruled that the government could be held liable for the claims, but the 10th U.S. Circuit Court of Appeals reversed that ruling in April. The appeals court said the government's actions amounted to an exercise of "discretionary functions" and as such were exempt from suit under the Federal Tort Claims Act.

In other action yesterday, the justices:

Refused to reinstate the murder convictions of former boxer Rubin (Hurricane) Carter and a codefendant, John Artis, over a triple murder in a Paterson, N.J., bar in 1966. The court let stand a ruling that the convictions were unlawful because prosecutors concealed important information from defense lawyers.

The case generated a substantial following over the years -- including a song by Bob Dylan that accused law enforcement officials of racial prejudice.

Both men were convicted of murder at their first trial but the convictions were overturned. They were convicted again after a second trial in 1976 and those convictions were also overturned on appeal.

Carter, who was once a contender for the middleweight boxing championship, was freed from prison in 1985 after serving 19 years. Artis had been paroled but was returned to jail last August on unrelated drug and weapons convictions.

A Passaic County, N.J., prosecutor said yesterday that a decision about whether to retry Carter and Artis would be made in the next two weeks, but Carter's attorney said he felt it was unlikely the state would ask for another trial.

Agreed to decide whether a ban on picketing of private residences can be squared with free-speech protections under the First Amendment. The high court said it would hear a case from the Milwaukee suburb of Brookfield, Wis., which banned all picketing in residential areas.

The case, Frisby v. Schultz, involves picketing in 1985 by antiabortion demonstrators in front of the home of a doctor who allegedly performed abortions as part of his medical practice in Milwaukee. A decision is expected by the end of the court's term this spring.

Agreed to decide whether the federal government may be held liable for damages caused by vaccines it licenses. The case, Berkovitz v. U.S., involves a Pennsylvania boy who contracted polio after his pediatrician gave him an oral polio vaccine in 1979.

The boy's parents sued the government, claiming it was negligent in its 1963 decision to license Lederle Laboratories' Sabin oral polio vaccine and in its subsequent approval of the release of a specific lot of that vaccine.

The 3rd U.S. Circuit Court of Appeals ruled that the government may not be sued under these circumstances.

The Reagan administration, although it agreed with that ruling, asked the high court to hear the case in order to clarify disagreements among circuit courts on the extent of the government's immunity from such lawsuits.