On Thanksgiving night, the sounds of gunshots inside an Alabama mall sent shoppers diving for cover and sprinting for exits. Outside the mall, Emantic Fitzgerald Bradford Jr. pulled out a gun and rushed to protect shoppers, his family said.

But Mr. Bradford was soon dead. An off-duty police officer working security at the mall, Riverchase Galleria in Hoover, Ala., fatally shot him, the authorities said. In the days that followed, the official account by the Hoover Police Department of what happened inside and outside the mall has shifted drastically.

At first, the officer was praised for stopping a gunman after two people were shot outside a Footaction store on the second floor. Then the police said that Mr. Bradford was not in fact the gunman and that the true gunman remained on the loose.

Early Monday morning, the Police Department made another statement. “With certainty Mr. Bradford brandished a gun during the seconds following the gunshots,” the statement said, adding that his actions had “instantly heightened the sense of threat to approaching police officers responding to the chaotic scene.”