CHICAGO — The Chicago police, facing almost daily protests and a newly announced Justice Department investigation, released footage Monday night showing a 38-year-old black man being shocked by a Taser and dragged down a hallway by officers in 2012.

The man, Philip Coleman, later died at a hospital. A county medical examiner noted trauma on Mr. Coleman’s body, but said his death had been caused by an allergic reaction to a medication given at the hospital. A lawyer for the Coleman family said he believed the repeated shocks contributed to Mr. Coleman’s death.

The officers’ treatment of Mr. Coleman, a college graduate whose family said he was having mental health problems, received a withering rebuke from Mayor Rahm Emanuel, whose handling of other police use-of-force cases has prompted calls for his resignation, and who has announced a series of policy changes and personnel moves in recent days as pressure mounted.