The Supreme Court's long-running debate over the meaning of federalism took a new turn in a case the justices heard on Monday.

The question was, What happens when a state chooses to give criminal suspects more protection than the federal Constitution requires? If an arrest is improper under state law, does that mean that a search the police conduct in connection with the arrest is necessarily improper as well, even if the arrest met constitutional standards?

It is a question that has divided courts around the country, since it is not unusual for states to offer more vigorous protection for individual rights, either by their own constitutions or by statute, than that provided by the federal Constitution, as interpreted by the Supreme Court.

In this case, the police in Virginia arrested a man for driving with a suspended license. Under Virginia law, that offense is a misdemeanor that does not justify an arrest, except in unusual circumstances. Ordinarily, the police are limited to issuing a summons and a notice to appear in court.

Nonetheless, the police took the man, David L. Moore, into custody and in the search that followed found 16 grams of crack cocaine (about a half ounce) and $516 in cash. Mr. Moore was convicted of the drug offense and sentenced to five years in prison. The Virginia Supreme Court dismissed all charges, ruling that because the arrest was unlawful, so was the search.

Under the United States Supreme Court's precedents, searches that are "incident to a lawful arrest" are considered valid. During the argument on Monday, there was general agreement that the arrest itself was supported by probable cause, the standard under the Fourth Amendment of the Constitution. But given the state law, could the arrest be considered "lawful"?

Arguing for Virginia, which was appealing a decision by its state Supreme Court, Stephen B. McCullough said that "there was a violation of state law, but it wasn't a constitutional problem."

Mr. McCullough, a deputy state solicitor general, told the justices: "You have clear rules. Why would you trade them in for a morass? An arrest is constitutional if the officers have probable cause to believe a crime has been committed."

The rules were actually not quite so clear. Michael R. Dreeben, a deputy United States solicitor general who argued for the Justice Department in support of Virginia, told the justices that "admittedly, I think neither side is able to point to a case that squarely addressed and conclusively resolved the issue that's before the court."

Nonetheless, Mr. Dreeben maintained that it would be counterproductive to declare a search to be unconstitutional under these circumstances. "It's clear that imposing such a Fourth Amendment rule would do nothing other than discourage the states from providing additional restrictions as a matter of their own state's law that may serve to protect citizen privacy interests above the floor that this court has identified as required," he said.

Thomas C. Goldstein, arguing for the defendant, told the justices that under English common law, an illegal arrest was considered a form of trespass. "Because at common law you could not search someone pursuant to an arrest that was a trespass," he said, "the search itself is unconstitutional."

Chief Justice John G. Roberts Jr. was not persuaded. "It's not a lawful arrest," he said. "But that's a different question than whether or not it is an arrest. Our precedents say if it's an arrest, you can search ‘incident to the arrest.' "

"I disagree," Mr. Goldstein said. The court's precedents, he continued, indicated "that it has to be an arrest that is lawful under state law." The case came down to a simple concept that would be easy to administer, Mr. Goldstein said: "A rule that simply says to the police officer, ‘If you're allowed to arrest him, arrest him; if you're not, you're not, and you can't search him constitutionally.' "

Several justices pressed Mr. McCullough, Virginia's lawyer, on where, given a variety of dubious arrests, he would draw the line between valid and invalid searches. Justice Antonin Scalia asked whether, as a Supreme Court justice, he could search a neighbor's house on suspicion that marijuana was being grown there.

Yes, if the justice, as a federal employee acting on behalf of the government, had probable cause, Mr. McCullough said.

How about a "federally employed janitor?" Justice Scalia asked. "His neighbor is growing marijuana, and he's just as offended as a Supreme Court justice would be. Can he conduct a search?"

The lawyer replied, "I think if he's doing it on behalf of the state, the answer is yes."

Justice Scalia said, "Wow."

The case is Virginia v. Moore, No. 06-1082.