The Supreme Court ruled 6 to 2 yesterday that Indian tribal courts lack inherent power to try and punish non-Indians for crimes.

"The power of the United States to try and criminally punish is an important manifestation of the power to restrict personal liberty," Justice William H. Rehnquist wrote in the opinion for the court.

"By submitting to the overriding sovereignty of the United States, Indian tribes therefore necessarily give up their power to try non-Indian citizens of the United States except in a manner acceptable to Congress," he said.

The court acted in a case in which the Suquamish Indian tribe, whose reservation is on Puget Sound across from Seattle, arrested and moved to prosecute two non-Indian residents, Mark D. Oliphant and Daniel B. Belgrade.

But the cast has importance far beyond Puget Sound. Of the 127 reservations with court systems that exercise criminal jurisdiction, 33 in addition to the Suquamish claim authority over non-Indians as part of their tribal self-government.

On many of the reservations, non-Indians are a substantial proportion or even a majority of the resident populations. In some cases, non-Indians visit in substantial numbers.

In addition, the decision poses a practical problem: at some reservations, federal law-enforcement officials are unavailable or inconveniently located, while state authorities lack jurisdiction.

For the court, Rehnquist recognized that some Indian tribal court systems have become "increasingly sophisticated" that the Indian Civil Rights Act of 1968 "extends certain basic procedural rights to anyone tried in Indian tribal court," and that there is a "prevalence of non-Indian crime on today's reservations which the tribes forcefully argue requires the ability to try non-Indians."

"But there are considerations for Congress to weigh in deciding whether Indian tribes should finally be authorized to try non-Indians," the justice wrote. "They have little relevance to the principles which lead us to conclude that Indian tribes do not have inherent jurisdiction to try and punish non-Indians."

The decision reversed the 9th U.S. Circuit Court of Appeals. Justice Thurgood Marshall, in a dissent, said that because no treaty or law has withdrawn the right of tribes to try and punish all persons who commit offenses on reservations, the right remains "a necessary aspect of their retained sovereignty . . ."

Chief Justice Warren E. Burger joined Marshall Justice William J. Brennan Jr., who was ill when the case was argued, did not participate.

The charge against Oliphant was that he had assaulted a tribal officer and resisted arrest during the Suquamish's annual celebration of Chief Seattle Days. Belgrade was arrested after an alleged high-speed race along reservation highways that ended with a collision with a tribal police car.