The records show that the officers’ managers at times appeared at disciplinary hearings to praise the work of the officers. At Mr. Haley’s hearing, a lieutenant spoke on his behalf, saying he was “a hard-working officer” who “routinely makes good decisions.” At Mr. Martin’s hearing, records show, a lieutenant called him among the “top producers.”

All five officers were fired this month after Mr. Nichols’s death. Video from his arrest on Jan. 7 showed officers kicking, pepper-spraying and punching him. He was taken to a hospital and died three days later.