ASHINGTON, March 22 — A Nevada rancher's refusal four years ago to tell a deputy sheriff his name led to a Supreme Court argument on Monday on a question that, surprisingly, the justices have never resolved: whether people can be required to identify themselves when the police have some basis for suspicion but lack the probable cause necessary for an arrest.

The answer, in a case that has drawn intense interest from those who fear increased government intrusion on personal privacy, appeared elusive.

"A name itself is a neutral fact" that is neither incriminating nor an undue invasion of privacy, Conrad Hafen, Nevada's senior deputy attorney general, told the court in defense of a state statute that requires people to identify themselves to the police if stopped "under circumstances which reasonably indicate that the person has committed, is committing or is about to commit a crime."

"It's a neutral fact that I'm wearing a pinstripe suit," Justice David H. Souter told Mr. Hafen. But if someone who had just robbed a bank was reported to be wearing a pinstripe suit, that fact if reported to the police might no longer be so neutral, Justice Souter added.

The Bush administration joined the state in defending the statute.

Lawyers for Larry D. Hiibel, who is appealing his conviction for violating the Nevada law, raised two constitutional challenges to the identification requirement: that it amounts to an illegal search under the Fourth Amendment and that it compels self-incrimination in violation of the Fifth Amendment.

The Nevada Supreme Court upheld Mr. Hiibel's conviction, a misdemeanor, and rejected his constitutional challenge to the state law.

Standing by his pick-up truck on a rural road, he had been approached by a deputy sheriff who was investigating a passing motorist's report that a man in the truck had been hitting a woman. Mr. Hiibel's adult daughter was in the cab of the truck .

The deputy, Lee Dove, asked Mr. Hiibel 11 times for identification. Mr. Hiibel, saying he had done nothing wrong, refused to give his name and challenged Deputy Dove to arrest him. Eventually, the deputy did arrest him. A videotape of the incident, captured by a camera in the squad car, is on Mr. Hiibel's Web site, www.hiibel.com. Mr. Hiibel was never charged with any criminal offense beyond his refusal to identify himself.

A landmark Supreme Court ruling in 1968, Terry v. Ohio, gave the police the authority to briefly detain, question and conduct a pat-down search of someone whose activities — casing a Cleveland storefront, in that case — gave rise to "reasonable suspicion," short of probable cause for a formal arrest. There is no dispute that the encounter between Mr. Hiibel and Deputy Dove was a "Terry stop" within the meaning of that decision. The dispute in Hiibel v. Sixth Judicial District Court, No. 03-5554, is over Mr. Hiibel's response, or lack of response.

Robert E. Dolan, Nevada's deputy state public defender, told the justices that while the deputy "certainly had the right to ask" Mr. Hiibel for his name, "equally so, Mr. Hiibel had the right not to respond."

Justice Antonin Scalia was openly skeptical. "What is the meaning of Terry?" he asked. Did Mr. Dolan mean that the police were "allowed to ask questions but shouldn't expect answers?"

Yes, the public defender replied; the state should not be permitted to criminalize silence or to "extract data from a person."

Justice Stephen G. Breyer appeared to agree, suggesting a rule under which the police can ask but the citizen does not have to answer. "Everyone can understand that," Justice Breyer said, adding, "Why complicate this thing?" Several Supreme Court decisions over the years have suggested such a rule, but there has never been a formal opinion to that effect.

One of the Fourth Amendment questions in the case is whether a person's refusal to answer a seemingly benign identity question can convert a police officer's "reasonable suspicion" into probable cause to make an arrest. Only Justice Scalia appeared to endorse that prospect. "I would think any reasonable citizen would answer," he observed.

One of the many wrinkles in the case is that once a person is arrested, the right to remain silent is guaranteed by the Fifth Amendment. To that extent, a person who falls under a lesser degree of suspicion might be seen as having less constitutional protection. Another wrinkle is that there is no claim that the police cannot run a check on a license tag or — if the suspect is driving — ask to see the driver's license. In this case, Mr. Hiibel's daughter was behind the wheel, Mr. Hiibel was outside the truck, and the case was not treated as a traffic investigation.

As a matter of Fifth Amendment analysis, one question is whether giving one's name is sufficiently "testimonial" to invoke the constitutional protection against self-incrimination. "The question, it seems to me, is whether a name itself has intrinsic testimonial consequences," Justice Anthony M. Kennedy told Mr. Dolan, the public defender.

If it did not, Mr. Dolan replied, "the government could require name tags."

In briefs filed with the court, civil liberties groups warned that a rejection of Mr. Hiibel's claim to privacy could open the door to such measures as national identification cards. One group, the Electronic Privacy Information Center, said that government databases were now of such "extraordinary scope" that "systems of mass public surveillance" could result from a ruling that authorized "coerced disclosure of identity."

But the justices appeared eager to avoid a broad ruling and to confine their eventual decision to the specific context of a suspected crime. "We're all concerned about national ID cards and all that kind of stuff," Justice John Paul Stevens said at one point.