Mr. McClinton appeared voluntarily at the Greenville Police Department, where he made statements that implicated him in the crime on Wednesday, Mr. Strain said. He did not have a lawyer as of Wednesday night and was to make his first court appearance on Thursday.

Noting that the investigation was continuing, Mr. Strain declined to discuss a possible motive for the arson or how investigators linked him to it.

The fire was set a week before Election Day, but a state official said the authorities did not believe it was motivated by politics.

“There may have been some efforts to make it appear politically motivated,” Mike Chaney, who is the Mississippi insurance commissioner and the state fire marshal, told The Associated Press.