WASHINGTON — The Supreme Court on Monday ruled for an Arizona police officer who shot a woman outside her home in Tucson. The court’s decision was unsigned and issued without full briefing and oral argument, an indication that the majority found the case to be easy.

In an impassioned dissent, Justice Sonia Sotomayor said the majority had gone badly astray.

“Its decision is not just wrong on the law; it also sends an alarming signal to law enforcement officers and the public,” she wrote. “It tells officers that they can shoot first and think later, and it tells the public that palpably unreasonable conduct will go unpunished.”

The case started in 2010 when three police officers responded to a 911 call reporting that a woman had been seen acting erratically by hacking at a tree with a knife.

They saw Sharon Chadwick standing in the driveway of a house. A second woman, Amy Hughes, emerged from the house, holding a kitchen knife. She stopped six feet from Ms. Chadwick.