It’s also the latest setback for a department that is in the midst of its deadliest 30-day stretch since 2015, with 43 people killed in the past month. The department also has seen a number of high-profile departures, including a top commander who resigned last week after slamming a chair into a wall during a meeting, and its chief spokesman, T.J. Smith, who resigned, citing an unstable environment — with “mudslinging” within the department and “political turmoil” all around it — as the driving force behind his decision.