There are no laws in the State of New York prohibiting the police from using a choke-hold though there are in other jurisdictions. As a matter of policy the NYPD prohibits the use. So the answer would be no they cannot. However because it isn't illegal for them to use one a criminal proceeding based solely on the choke-hold will go nowhere. It becomes an NYPD administrative issue and the most the NYPD can do is fire the guy and possibly take action against his pension. That's it.
Of course the family can, and should, and will, bring a civil action, but that's against the city - the taxpayers - and not the cop. The NYPD pays a hundred million or so a year to settle civil cases against it. If for no other reason the people should be screaming for change because of that alone.
Of course the police are treated differently. They ultimately cannot do their job if they can't force compliance with their legal orders. That doesn't mean that force should be first resort as it was here. It should be
the last resort.