He can still be tried if he is found to be mentally fit at some point. Otherwise there’s a good chance he may spend many years in the mental institution.
Often in cases like this where nobody was actually hurt, the prosecutors will agree to drop the charges in exchange for some type of supervised release overseen by the docs at the mental institution, and he may be required to receive outpatient treatment with regular reporting to the judge.
Even if he is subsequently found fit to stand trial (i.e. - able to understand the proceedings and to give instructions to his lawyer), there would still be the issue whether he was mentally compétant at the time of the offence. If not, he may have a valid defence of mental incompetence, based on New York State law.