Denying criminal defendants their constitutional right to cross-examine prosecution witnesses is not necessarily grounds to overturn their convictions, the Supreme Court ruled yesterday.

Justice William H. Rehnquist, writing for the majority, said a Delaware judge should have allowed a murder suspect to question a witness about a deal the witness had made with the prosecution in exchange for his testimony.

But that mistake may have been "harmless error," Rehnquist said in sending the case back to the Delaware Supreme Court to see if the mistake made any difference in the eventual conviction of Robert E. Van Arsdall for murder in 1982.

Rehnquist said "some constitutional errors -- such as denying a defendant the assistance of counsel at trial . . . are so fundamental . . . that they require reversal without regard to the facts or circumstances of the particular case."

"Whether such an error is harmless in a particular case depends upon a host of factors," Rehnquist said, including the importance of the witness' testimony and the overall strength of the prosecution's case.

The 7-to-2 ruling in Delaware v. Van Arsdall overturned the Delaware Supreme Court's decision that the judge's actions required the conviction to be thrown out no matter what effect the actions had on the case.

Justice Thurgood Marshall, in dissent, argued that the Delaware high court's actions were correct. Justice John Paul Stevens, in a separate dissent, argued that the Delaware high court had the authority to throw out the conviction and the justices should defer to the state court.

In other action yesterday, the court declined to get involved in a growing controversy over prosecutors' use of subpoenas against defense lawyers to compel them to testify about the fees they receive from their clients.

Defense lawyers argue that such subpoenas, seeking fee information to use either as evidence or to force forfeiture of illegal profits, violate defendants' rights.

In two cases yesterday, Roe v. U.S. and Doe v. U.S., the court, without comment, let stand appeals court rulings that required defense lawyers to testify before grand juries.

The 2nd U.S. Circuit Court of Appeals last year ruled that a lawyer representing alleged mobster Anthony Colombo must tell a federal grand jury in New York investigating organized crime about his fee arrangements with Colombo.

The 4th U.S. Circuit Court of Appeals ruled last year that a lawyer who had represented a narcotics defendant in court here five years ago must testify to a grand jury in Maryland investigating possible tax fraud by the defendant.

In other action, the court:

*Ruled unanimously that federal judges, not arbitrators, must decide whether some collective bargaining fights are to be resolved by arbitration. Justice Byron R. White, writing for the court in AT&T Technologies, Inc. v. Communications Workers of America reversed a ruling by a federal appeals court in a case involving layoffs of 79 telephone installers.

*Ruled unanimously that the secretary of energy may put rates for hydroelectric power generated at federally owned dams into effect on an interim basis pending review by the Federal Energy Regulatory Commission. The opinion by Justice Marshall in U.S. v. City of Fulton reversed a ruling by the U.S. Court of Appeals for the Federal Circuit that ordered refunds of $954,816 to three Missouri cities.

*Agreed to decide next term whether police, entering a Phoenix apartment to investigate a shooting, could check serial numbers on expensive stereo equipment to see if it is stolen and then use that evidence to substantiate robbery charges. The case, Arizona v. Hicks, asks the court to allow the use of such evidence if it is in "plain view" of officers when they are properly investigating a crime.