YOU are the boss of the police, got that? You dont need the 'support' of the police. They need to show you obedience. You need to show the police who is boss. They are there to obey your commands. You're in charge. You're accountable. You're responsible. And if any cop doesnt like it, fire their ass and get new ones. This isn't complicated: cops can't go around killing people. Period.
The Medical Examiner says this was a homicide. So fire the cop responsible, arrest him, and turn him over to the District Attorney. This shit is simple. If the DA on Staten Island declines to prosecute, thats on him, not you. You've done your job.
Obviously theres some incompetence in the control of this precinct. Fire the commander and appoint a new skipper. Bring some accountability to this thing and you will have everyones support. Lynch and the union will complain. So the fuck what. Fuck him. He's a Republican anyway. You give them a choice: raise and a contract, or nothing and Lynch. They'll put Lynch in a choke hold pronto.
The problem here is not Broken Windows policing, which is effective and needed. The problem is bad cops who think that killing people is just part of the arsenal of tools for effective law enforcement. You need to make this an issue of bad cops, not bad policing.
Put loudmouth people like Sharpton in their place: on fucking TV. Not sitting right next you like a public official. What the fuck is wrong with you? Sharpton and Rubenstein will get their photo op (and percentage $$$$) at the settlement news conference. Dont waste your time entertaining his bullshit.
You're the Mayor. You're in charge. You sort it out and make it happen. But this weak, silly, shiftless, dumb PR game isn't helping anybody, least of all YOU.