The authorities released surveillance video on Monday that showed the moment when a city commissioner in Lakeland, Fla., fatally shot a man who he believed had just stolen a hatchet from his store.

The Lakeland Police Department and the State Attorney’s Office for the 10th Judicial Circuit are investigating the Oct. 3 shooting and expect to be finished by the end of the week. No charges have been filed against Michael Dunn, a city commissioner in Lakeland, which is about 35 miles east of Tampa. He took office in January.

The Lakeland Police Department, which responded to the shooting, released the video after it received several inquiries.

“We just felt that keeping it secret any longer did not benefit the investigation,” Jacob Orr, an assistant state’s attorney, said of the release of the video in an interview on Monday.