WASHINGTON -- The U.S. Supreme Court struggled yesterday with the question of whether the right to remain silent includes the right not to divulge your name to police if they lack probable cause that you have committed a crime.

The debate among the justices occurred during oral arguments in the case of a Nevada rancher who refused to identify himself when stopped on suspicion that he might be physically abusing his daughter.

In reviewing the misdemeanor conviction of Larry "Dudley" Hiibel, the justices seemed divided over whether identifying oneself is a "neutral act," as a lawyer for the state argued, or a potentially incriminating admission.

"One's name is not incriminating one way or another," Justice Sandra Day O'Connor suggested.

But Justice David Souter said everything depended on the context. "It's a neutral fact that I'm wearing a pinstripe suit," he said, but if a suspect in a crime were observed wearing such a suit, it could become valuable evidence.

That is exactly what Hiibel's lawyers argued in challenging his conviction under a Nevada law that makes it a misdemeanor for a citizen stopped on "reasonable suspicion" -- a lesser standard than the "probable cause" needed for arrest -- to refuse to identify himself.

In 2000, an informant told sheriff's deputies that a man standing outside a pickup truck had struck a young female passenger in the truck. A deputy found Hiibel standing outside the truck and his 17-year-old daughter, Mimi, sitting inside.

Under Nevada law, an assault on a family member is punished more severely than other assaults. Hiibel, by giving his name, would have been establishing a family relationship and thus would have made himself potentially vulnerable to the stiffer penalty.

Hiibel repeatedly refused to identify himself to the deputy, was arrested and eventually convicted of the misdemeanor of "delaying an officer." Initially, he was also charged with domestic battery, but that charge was dropped for lack of evidence. (In fact, Hiibel said, it was his daughter who punched him in his arm.)

Yesterday, Hiibel's lawyer, Robert E. Dolan, argued that under the self-incrimination clause of the Fifth Amendment, "no American citizen has an obligation to answer" questions posed by the police, including a request for the citizen's name. "The government cannot criminalize a non-response," Dolan said.

Hiibel also has argued that compelling him to disclose his name violates his Fourth Amendment rights to be free from unreasonable searches and seizures.

But Nevada Senior Deputy Attorney General Conrad Hafen told the court that requiring someone in Hiibel's position to provide his name -- a "neutral act" -- is a minor intrusion when weighed against the state's interest in protecting a police officer's safety and providing effective law enforcement.

Lending support to Nevada, Sri Srinivasan of the U.S. Solicitor General's Office told the court that the name of someone stopped for questioning could provide "crucial information" -- for example, a link to electronic records showing that he had committed past crimes.

Three justices -- O'Connor, Chief Justice William Rehnquist and Justice Antoinin Scalia -- seemed skeptical of Hiibel's claim. "Why is it a violation of the Constitution to ask someone to do something any responsible citizen would do?" Scalia asked Dolan.

Rehnquist wondered how police could ever solve a murder case if they couldn't ask potential witnesses to identify themselves.

Justice Ruth Bader Ginsburg, while not as skeptical of Hiibel's argument as some of her colleagues, observed that "we treat names differently" from other information. She noted that federal law requires young men to register by name for the standby military draft.

Hiibell found some sympathy from other members of the court. Justice Anthony Kennedy said he took the Fifth Amendment argument seriously because "this person was certainly under suspicion of criminal activity."

Justice Stephen Breyer suggested to Hafen, the Nevada prosecutor, that in previous cases, "each time the court said there's no obligation to respond" to a question posed by a police officer who lacks probable cause. "You can ask," Breyer said, "and he doesn't have to answer."

That is what would happen in Pittsburgh if a suspect were to refuse to give his name, and police lacked probable cause to arrest him, city Police Chief Robert W. McNeilly Jr. said. Since Pennsylvania doesn't have a law like Nevada's, he said, police would file a report and try to ascertain the suspect's identity in some other way.

Hiibel, who was in the courtroom for yesterday's arguments wearing a cowboy hat, said he was encouraged by what he heard from the bench and was unimpressed by the state's presentation. "They didn't have much of an argument," he said.