ST. PAUL — The Minnesota Supreme Court on Wednesday upheld a state law making it illegal for suspected drunken drivers to refuse a breath test.

The high court rejected a man’s claim that the law violated due process by preventing him from refusing an unconstitutional, warrantless search.

The case stemmed from the 2012 arrest of William Robert Bernard, whom witnesses identified as the driver of a truck that became stuck on a boat launch. Police said Bernard smelled of alcohol and acknowledged drinking but refused a chemical test after he was arrested on suspicion of drunken driving.

Justices wrote that a search following a lawful arrest is a well-recognized exception to the requirement of a search warrant. They also wrote the law furthers the state’s ability to prosecute drunken drivers.

In the majority opinion, Chief Justice Lori Gildea said that the breath test “was a search of Bernard’s person that would have been no more intrusive than the myriad of other searches of the body that we and other courts have upheld as searches incident to a valid arrest.”

Gildea said criminalizing a refusal to submit to testing is “rational,” Minnesota Public Radio News reported.

The American Civil Liberties Union of Minnesota had submitted a brief arguing that it is unconstitutional to apply criminal penalties to drivers solely because they refused a search without a warrant.

ACLU-MN executive director Charles Samuelson said his organization, which was not representing Bernard, was disappointed by the ruling. He said the court had set “a dangerous precedent.”

“Imagine if the police could charge us with a crime if we refused to allow them into our houses without a warrant,” Samuelson said in a statement. “People would be outraged.”

In 2013, the U.S. Supreme Court ruled that police usually must try to obtain a search warrant from a judge before ordering blood tests for drunken-driving suspects.