N.Y.C. Admin. Code § 9-125: § 9-125 Civil jail.

a. The commissioner of correction shall have custody of civil prisoners and the prisons wherein they are confined.

b. The commissioner of correction may keep in any place or places under the commissioner's jurisdiction persons lawfully committed to his or her custody without regard to the county wherein such persons may have been arrested. Any such person who is entitled to the liberties of the jail must be admitted to the jail liberties of the county wherein such person was originally arrested.