N.Y. Correct. Law § 501

§ 501. Jail physician. 1. The board of supervisors of each county,\nexcept New York, must appoint some reputable physician, duly authorized\nto practice medicine, as the physician to the jail of the county. If\nthere is more than one jail they must appoint a physician to each. The\nphysician to a jail holds his office at the pleasure of the board which\nappointed him, except in the county of Kings. In that county, the term\nof his office is three years.\n 2. Notwithstanding subdivision one of this section, a county board of\nsupervisors may instead procure the services of a professional\npartnership, a professional service corporation, a professional service\nlimited liability company or a registered limited liability company,\nduly authorized to practice medicine in the state, for the purpose of\nproviding health services to the inmates of the jail, provided that one\nphysician from any such professional partnership, professional services\ncorporation, professional service limited liability company or\nregistered limited liability company shall be designated by the board to\nact as the chief medical officer of the jail.\n