N.Y. Correct. Law § 611-a

§ 611-a. Commitments to county or regional correctional institutions.\n1. Any commitment to a county or regional correctional institution\npursuant to subdivision two of section 70.20 of the penal law shall be\ndeemed a commitment to the county jail, workhouse or penitentiary, or to\na penitentiary outside the county in the case of an agreement pursuant\nto section four hundred eighty of this chapter, as the case may be, and\nthe order of commitment shall specify the institution in which the\nsentence is to be served.\n 2. Nothing in this section shall affect or limit any other provision\nof law with respect to transfers of persons so committed.\n