The authorities in Michigan said that a man ripped out yard signs supporting former President Donald J. Trump and then used an all-terrain vehicle to run over an 80-year-old man who was putting them back up, leaving the victim in critical condition.

The attack on Sunday, just over a week after an assassination attempt on Mr. Trump, was one of three politically motivated incidents involving the suspect this weekend in Hancock, Mich., a small town in the state’s Upper Peninsula, the local authorities said.

The man also used a shovel to destroy the windows of a parked truck with a sticker supporting Mr. Trump, the officials said, and vandalized the tires of a parked vehicle with a sign supporting law enforcement.

The suspect, whose name was not released, lived in the area. Tami Sleeman, the Hancock police chief, said the suspect, who was 22, left a message with the Police Department saying he wanted to confess to an attack, but killed himself before officers arrived at his home.

Michigan is a swing state that both Mr. Trump and Vice President Kamala Harris hope to carry in November.

This is a developing story. Check back for updates.