ASHINGTON, June 21 - People who have given the police some reason to suspect that they may be involved in a crime can be required to identify themselves unless their very name would be incriminating, the Supreme Court ruled Monday in a case that had raised concerns about the boundaries of personal privacy.

The 5-to-4 decision addressed a question that, surprisingly, had gone unresolved for decades. But the answer the court gave was hardly definitive, leaving for another day some of the more difficult issues of application.

The case was a challenge by a Nevada rancher to a state law requiring people stopped in suspicious circumstances to identify themselves on the request of a police officer. Twenty states, including New York, have such laws on their books, as do a number of cities and towns.

The rancher, Larry D. Hiibel argued that his Fourth Amendment right against unreasonable search and seizure and his Fifth Amendment right against compelled self-incrimination were violated by the state law. Mr. Hiibel's cause was taken up by an array of groups concerned with privacy in an age when a name entered in an electronic database can provide a sometimes startling amount of personal information.

Justice Anthony M. Kennedy's majority opinion rejected both constitutional arguments, at least as they applied to Mr. Hiibel. As a Fourth Amendment matter, Justice Kennedy said, the demand to identify oneself is a logical corollary to the circumstances of a valid police stop, as described by the court in a 1968 decision, Terry v. Ohio.

That decision permits a police officer to briefly detain, question and conduct a pat-down search of a person whose behavior has given rise to "reasonable suspicion," short of the probable cause necessary for a formal arrest. Such an encounter is widely known as a "Terry stop."

"Obtaining a suspect's name in the course of a Terry stop serves important government interests," Justice Kennedy said. "The request for identity has an immediate relation to the purpose, rationale and practical demands of a Terry stop," he added.

But as Justice Kennedy pointed out, in the 36 years since the Terry decision, the court, while permitting a police officer to question a suspect, had never explicitly decided whether the suspect had to answer or could be arrested and prosecuted for refusing. He acknowledged that a number of opinions, including a concurring opinion by Justice Byron R. White in the Terry case itself, had indicated that there was not an obligation to respond. But "we do not read these statements as controlling," Justice Kennedy said, as long as the request for identification is made in the context of a valid Terry stop.

In this case, Hiibel v. Sixth Judicial District Court, No. 03-5554, the request by a deputy sheriff for Mr. Hiibel's name was valid, Justice Kennedy concluded. The deputy had responded to a telephone report of a man hitting a woman in the cab of a truck parked along a rural road. Arriving to investigate a possible domestic assault, the deputy found a man who turned out to be Mr. Hiibel standing outside the truck, with a young woman sitting inside the cab. She turned out to be his daughter.

Eleven times, the deputy asked Mr. Hiibel for identification, and 11 times, he refused to provide it. The incident was caught by a video camera on the deputy's car, and can be seen on Mr. Hiibel's Web site, www.hiibel.com, along with Mr. Hiibel's description of the events and the following description of him: "He lives a simple life, but he's his own man."

Eventually, Mr. Hiibel was arrested and charged with the misdemeanor of refusing to identify himself. He was convicted and fined $250. The Nevada Supreme Court upheld his conviction.

In the ruling on Monday, the majority's analysis of Mr. Hiibel's Fifth Amendment challenge to the law was more ambiguous than the Fourth Amendment discussion. Mr. Hiibel argued that his conviction violated his Fifth Amendment right against compelled self-incrimination. But "in this case disclosure of his name presented no reasonable danger of incrimination," Justice Kennedy said, and so the case did not test the Fifth Amendment limits of a compelled-identification law.

Justice Kennedy's basis for that conclusion was that Mr. Hiibel seemed to have nothing to hide, refusing to identify himself "only because he thought his name was none of the officer's business," the opinion said. Justice Kennedy noted that "answering a request to disclose a name is likely to be so insignificant in the scheme of things as to be incriminating only in unusual circumstances."

He continued: "Still, a case may arise where there is a substantial allegation that furnishing identity at the time of a stop would have given the police a link in the chain of evidence needed to convict the individual of a separate offense." The court could decide such a case at that point, Justice Kennedy said.

This provoked a stinging dissent from Justice John Paul Stevens, who said there was no basis for assuming that names were generally nonincriminating or would not usually furnish a "link in the chain of evidence."

"Why else would an officer ask for it?" Justice Stevens said, adding, "Indeed, if we accept the predicate for the court's holding, the statute requires nothing more than a useless invasion of privacy."

In a separate dissenting opinion, Justice Stephen G. Breyer said that despite the lack of a formal precedent directly on the point, there was a "generation-old" understanding that people subjected to Terry stops were not required to answer any questions. There was no indication that this understanding "has significantly interfered with law enforcement," Justice Breyer said, and no reason to change it at this point. Further, he said, there was no way for "a police officer in the midst of a Terry stop" to know whether the situation was the ordinary one or the "special case where the majority reserves judgment."

Justices Ruth Bader Ginsburg and David H. Souter joined Justice Breyer's dissenting opinion. Justice Kennedy's majority opinion was joined by Chief Justice William H. Rehnquist and by Justices Sandra Day O'Connor, Antonin Scalia, and Clarence Thomas.

"A Nevada cowboy courageously fought for his right to be let alone but lost," the Nevada state public defender's office, which represented Mr. Hiibel at the court, said in a statement posted on Mr. Hiibel's Web site. Indeed, Mr. Hiibel, 59, became something of a folk hero in certain quarters in the months his case was pending before the court.

The Cato Institute, a libertarian research organization here, filed a brief on his behalf. Timothy Lynch, director of Cato's project on criminal justice, said in an interview on Monday that "the ruling makes it extremely difficult now for ordinary people to assert their constitutional rights against the government." Mr. Lynch said the court had "blurred the line between asserting your rights and committing the crime of obstruction of justice."

But Marc Rotenberg, executive director of the Electronic Privacy Information Center, which also filed a brief for Mr. Hiibel, said he was encouraged by the suggestion in the majority opinion that a demand for identification documents, as opposed to just a person's name, as in this case, would have raised a deeper constitutional issue. Given an anticipated debate over national identification cards, "we think that's good news," Mr. Rotenberg said. His organization's brief emphasized the amount of information currently available from interconnected databases.

With 4 cases decided Monday, the court now has 12 decisions to go before it can conclude its term, most likely by the end of next week. Among them are the three most closely watched cases of the term, asking the court to define the legal status of detainees held as enemy combatants at Guantánamo Bay, Cuba, and in a military prison in Charleston, S.C.