WASHINGTON (AP) _ The Supreme Court today said it will decide whether criminal suspects may be asked to give up the right to sue authorities in return for having the charges against them dropped.

The justices agreed to hear an appeal by Newton, N.H., officials seeking to enforce such an agreement.

Bernard E. Rumery Jr., a Newton businessman, was arrested in 1983 on charges of tampering with a witness.

Earlier that year, David Champney had been arrested and charged with felonious sexual assault. Champney was a former hunting companion of Rumery's.

The alleged rape victim, known to both Champney and Rumery, told police that Rumery had threatened her with harm if she did not try to have the charges against Champney dropped.

Prior to arresting Rumery, Newton police did not seek a sworn affidavit from the alleged rape victim and did not attempt to get any corroborating evidence against Rumery, who had no criminal record.

Rumery was arrested at his home May 12, 1983 in the presence of his wife. He was handcuffed and taken to the county jail.

Rumery's case was to have been presented to a state grand jury on June 13, but before that date prosecutors and Rumery's lawyer discussed the possibility of dropping the charges in return for Rumery's promise not to sue police or public officials in connection with his arrest.

Rumery signed such an agreement on June 6.

Ten months later, Rumery sued the town of Newton, Police Chief David T. Barrett and the town's three selectmen in federal court.

He sought monetary damages for violations of his constitutional rights, negligence, infliction of mental distress, false imprisonment and defamation.

A federal trial judge, after noting the agreement signed by Rumery, threw out his suit.

But the 1st U.S. Circuit Court of Appeals reinstated the lawsuit last Dec. 2.

''We hold that a covenant not to sue public officials for alleged deprivations of constitutional rights, executed in exchange for a decision not to prosecute criminal charges, is void as against public policy,'' the appeals court ruled.

City officials then sought Supreme Court review, contending that the appeals court's flat ban on such agreements ''places an unwarranted constraint on prosecutors.''