Akhil Reed Amar is a professor of law and political science at Yale. Neal K. Katyal is a former acting solicitor general of the United States, a professor of national security law at Georgetown and a partner at the law firm Hogan Lovells.

SOMETHING astonishing happened Monday: Antonin Scalia, the Supreme Court’s longest-serving member and one of its most conservative justices, joined three liberal justices in a sharply worded dissent arguing for the rights of criminal suspects.

The court decided, 5 to 4, that the Constitution permits the police to swab the cheeks of those arrested of serious crimes, and then do DNA tests on the saliva samples to see if the suspects are associated with other crimes. Justice Scalia joined three liberal justices — Ruth Bader Ginsburg, Sonia Sotomayor and Elena Kagan — in dissenting.

DNA is already revolutionizing law enforcement. The ability for police to use cheek swabs of arrestees rests on a threadbare majority. The closeness of the vote, and the unusual coalitions on either side, suggest that the matter is far from settled. Justice Samuel A. Alito Jr., who was part of the majority, rightly called the case, Maryland v. King, “perhaps the most important criminal procedure case that this Court has heard in decades.”

As prosecutors, police agencies and civil libertarians consider the ruling’s implications, Justice Scalia’s stark dissent — and the fact that President Obama’s two appointees to the court so far agreed with it — makes it worthy of scrutiny, even if he was on the losing side. His argument is deeply flawed, because he did not get his history quite right....