In counties contained within New York City and in counties that have a commissioner of correction who is responsible for detention of defendants in criminal actions, it is the duty of the commissioner of correction of such city or county to deliver the defendant forthwith to the proper institution in accordance with the commitment. In all other counties it is the duty of the sheriff to deliver the defendant forthwith to the proper institution in accordance with the commitment.
N.Y. Crim. Proc. Law § 430.30