N.Y. Comp. Codes R. & Regs. tit. 14, § 18.3 – Notification to appropriate director of prisoner's need for hospitalization.

(a) If a jail physician and a warden certify in writing that a prisoner in a jail is in such a state of mental health that he is in need of involuntary care and treatment and that, in their opinion, the prisoner should be removed to a psychiatric hospital for treatment, the warden shall immediately notify the director of community mental health services of the county or city where the jail is located. Such notification shall be in writing or, if given by telephone or orally, shall be confirmed in writing. A copy of the certification shall be filed at the jail and a copy shall accompany the notification.
(b) If there is no such director of community mental health services, notification shall be given to the director of a hospital operated by local government within such county or city that has been certified by the Commissioner of Mental Hygiene as having adequate facilities to examine defendants pursuant to article 730 of the Criminal Procedure Law (see section 9.2 of this Title). If there is no such hospital in the county or city in which the jail is located, the notification shall be given to the director of the State hospital operated by the Department of Mental Hygiene serving the county in which the jail is located.
Note:
In accordance with the requirement of section 508.(3)(b)(i) of the Correction Law, the Judicial Conference has approved section 18.3 of this Part.