First off, chokeholds are only prohibited by NYPD guidelines, not by law. So, legally, they don't constitute negligence. Regardless, even if they were illegal, using an illegal maneuver to subdue someone that results in their death is not negligence. It could be considered
imperfect self-defense, theoretically, but he wasn't really acting in self defense, he was just subduing the suspect.
The cop wasn't being negligent by using a chokehold. Negligence is the opposite of being careful, so either he intentionally used the chokehold and was reckless (in which case he could theoretically be up for involuntary manslaughter) or he meant to use a wrestling move (as I talked about in my post
here) and slid in which case he could
theoretically be up for negligent manslaughter, but they would have to prove that he was being careless when he made a mistake rather than simply making the mistake.