ASHINGTON, April 4 - The Supreme Court in recent years has drawn constitutional rules for the use of newly popular law enforcement techniques. The police need a warrant before aiming a heat-detecting device at a private home in an effort to find out whether marijuana is growing inside under high-intensity lights. The police do not need a warrant before permitting a trained dog to sniff a car, or a piece of luggage at an airport, in order to detect drugs.

Those precedents converged in a case from Texas that posed this question: Can the police bring a trained dog to stand outside a private home and sniff for drugs?

The lower courts have disagreed, and the Supreme Court decided on Monday to let the confusion linger. The justices did not take the case.

The court offered no explanation for declining to hear an appeal from a Houston man, David G. Smith, whose supply of methamphetamine in his garage was detected by a trained dog.

After the dog was walked up Mr. Smith's driveway and signaled the presence of drugs behind the lower corner of the garage door, the Harris County Sheriff's Department obtained a search warrant and found the drugs and other criminal evidence. A state appeals court rejected Mr. Smith's appeal, upholding his conviction and his sentence to 37 years in prison.

The Texas Court of Appeals issued its ruling in February 2004. That was nearly a year before the Supreme Court, in a ruling in January, upheld the use of a trained dog to sniff a car that had been stopped for a non-drug-related traffic violation. But the Texas court did cite a 1983 Supreme Court decision, the first to address the use of drug-detecting dogs, that upheld the sniffing of luggage at an airport.

The constitutional question in all such cases is whether the canine sniff is, under the circumstances, a search within the meaning of the Fourth Amendment; if so, it requires probable cause or a warrant. The court has never categorically held that a sniff is not a search, and although the justices on Monday made no law, the case itself offered a window into the growing use of trained dogs and some of the legal issues the practice raises.

In its 1983 airport decision, United States v. Place, the court suggested that the sniff was not a search in that setting because it "discloses only the presence or absence of narcotics" without requiring that the suitcase be opened. In the decision two months ago, Illinois v. Caballes, the court said that a dog's sniff of an automobile that had been lawfully stopped for speeding did not "implicate legitimate privacy interests."

In the appeal the court turned down on Monday, Smith v. Texas, No. 04-874, Mr. Smith argued that the most important precedent for understanding his case was one that did not involve dogs at all, but rather a thermal imaging device that the police use to detect distinctive patterns of heat produced by the indoor cultivation of marijuana.

In a 2001 decision, Kyllo v. United States, the court held that the use of this device, when trained on a private home, was a search that required a warrant. In his majority opinion, Justice Antonin Scalia said that the heat patterns could also reveal other kinds of personal behavior behind a home's walls. Justice Scalia noted that the home was what the framers of the Fourth Amendment had in mind when they barred "unreasonable searches."

In the appeal on Monday, Mr. Smith's lawyers told the court: "No distinction exists between a thermal-imaging device and drug-sniffing dog in that they are both sense-enhancing and permit information regarding the interior of a home be gathered which could not otherwise be obtained without physical intrusion into a constitutionally protected area."

In urging the justices to reject the appeal, the Harris County district attorney, Charles A. Rosenthal Jr., argued that the thermal imaging case was off the point. "The use of a drug detection dog does not constitute the use of any technology, let alone advanced technology," he said.

The district attorney's brief cited a variety of lower-court precedents that had upheld canine sniffs as not amounting to searches: in the common corridor of a hotel, outside an Amtrak sleeper compartment, outside an apartment door, at the exterior of a home. These activities were found not to "implicate Fourth Amendment concerns," he said, because "society clearly is not willing to recognize as reasonable or legitimate an expectation of privacy in the possession of narcotics."

One decision from the federal appeals court in New York that reached the opposite conclusion in 1985 should be ignored as a precedent, he said, because that decision "is 20 years old, yet it stands alone" and has not been adopted by other courts.