N.Y. Pub. Health Law § 322

§ 322. Local health officer; term of office; removal. 1. The term of\noffice of the health officer of a municipality shall be four years and\nhe shall hold office until his successor is appointed and qualifies.\n 2. (a) The health officer may be removed from office for just cause by\nthe local board of health or by the commissioner after a hearing upon\nnotice. Removal of the health officer by the local board of health shall\nbe subject to the approval of the commissioner.\n (b) Where a health officer has been appointed jointly, by two or more\nlocal boards of health, the power of a local board of health to remove\nthe health officer shall in such case be exercised jointly by the local\nboards participating in the appointment.\n