When police answered the domestic dispute call at the home of Janet and Scott Randolph in Americus, Ga., she told them where they could find his cocaine. An officer asked Scott Randolph for permission to search the house; he refused, but Janet Randolph said yes.

The police went in, found a straw covered in cocaine crystals and arrested Scott Randolph.

Yesterday, the Supreme Court heard oral arguments about whom the police should have heeded that July day in 2001 -- the husband who did not want them to enter his house or the wife, who did.

The court's ruling could have implications for police in the many instances in which they must deal with two or more quarreling occupants of a place officers want to search. In a friend-of-the-court brief supporting the Georgia police, the Bush administration told the court that the issue is of national importance because federal officers "frequently conduct searches of premises based on an occupant's consent."

Searches without warrants are allowed in such circumstances. But Georgia's Supreme Court agreed with Randolph that when homeowners are divided, the search cannot happen without a warrant. The straw was inadmissible, the Georgia court ruled, because one inhabitant's consent "is not valid in the face of the refusal of an occupant who is physically present at the scene."

Justice Sandra Day O'Connor was one of several justices who seemed to embrace that view yesterday.

She asked Georgia's senior assistant attorney general, Paula K. Smith, whether the normal social expectation was that "it's okay to let a stranger in over the express wishes of a spouse or cohabitant."

Smith replied that Scott Randolph had a "lowered expectation of privacy" in the jointly occupied home, and that police in the small town knew the couple well.

But Justice Ruth Bader Ginsburg joined O'Connor's questioning, asking whether it makes a difference that the person was a "temporary visitor." Janet Randolph had apparently gone to the house only to pick up belongings before moving out, Ginsburg noted.

Smith replied that the police had no way of knowing that.

O'Connor also took on Deputy U.S. Solicitor General Michael R. Dreeben when he rose to support Georgia's case. "You have a case here where the wife says, 'Come in,' and the husband who is right there says no," she said, a note of exasperation in her voice.

Scott Randolph's presence at the scene is important, because in past cases in which the court has held that a single inhabitant's consent is sufficient, only one inhabitant was available to talk to police.

The debate grew so intense that it even prompted a rare extended intervention by Justice Clarence Thomas, who says nothing at oral arguments. Alluding to a past case in which the court said police could use evidence that was voluntarily handed to them by a suspect's wife, he asked Thomas C. Goldstein, Scott Randolph's lawyer, a series of questions designed to show that the straw would have been admissible evidence if Janet Randolph had simply gone upstairs and fetched it for the police herself.

Taking a different tack, Justice Stephen G. Breyer depicted the case not as a test of Scott Randolph's privacy but of his wife's equal control over their home, saying that the court's decision might affect women's ability to summon police protection against spousal abuse.

"It's her house, too," he told Goldstein. He asked why Scott Randolph should have more of a right to keep police out than his wife has to allow them in.

Goldstein replied that actual cases in which that problem arises are rare, and that a woman would always have the option of meeting police outside the house.

The case is Georgia v. Randolph, No. 04-1067. A decision is expected by July.