N.Y. Correct. Law § 501

§ 501. Jail physician. 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