The Supreme Court said Monday that law enforcement authorities might need a probable-cause warrant from a judge to affix a GPS device to a vehicle and monitor its every move — but the justices did not say that a warrant was needed in all cases.

The convoluted decision (.pdf) in what is arguably the biggest Fourth Amendment case in the computer age, rejected the Obama administration’s position that attaching a GPS device to a vehicle was not a search. The government had told the high court that it could even affix GPS devices on the vehicles of all members of the Supreme Court, without a warrant.

“We hold that the government’s installation of a GPS device on a target’s vehicle, and its use of that device to monitor the vehicle’s movements, constitutes a ‘search,’” Justice Antonin Scalia wrote for the five-justice majority. The majority declined to say whether that search was unreasonable and required a warrant.

All nine justices, however, agreed to toss out the life sentence of a District of Columbia drug dealer who was the subject of a warrantless, 28-day surveillance via GPS.

Four justices in a minority opinion said that the prolonged GPS surveillance in this case amounted to a search needing a warrant. But the minority opinion was silent on whether GPS monitoring for shorter periods would require one.