(b) The chief executive officer of a county public welfare department, whether referred to as commissioner or by other title, shall be appointed in accordance with the provisions of section one hundred sixteen of the social welfare law. 4-a. Medical examiner. The board of supervisors in any county in which the office of coroner is abolished shall appoint a medical examiner. A certificate of such appointment shall be filed and recorded in the office of the county clerk. The medical examiner, before entering upon the duties of his office, shall take and file the prescribed oath of office and furnish and file the required undertaking. The medical examiner shall serve at the pleasure of the board of supervisors and his appointment may be revoked at any time by resolution of the board of supervisors and the filing of a certificate of such revocation in the office of the county clerk. The medical examiner shall be a resident of the county and a physician duly licensed to practice his profession in the state of New York and shall be a person determined by the board of supervisors as qualified to perform an autopsy and dissect dead bodies of human beings. 4-b. Coroner's physician. Except in counties where the office of coroner has been abolished, the board of supervisors may appoint one or more coroner's physicians or may provide by local law for the appointment of one or more coroner's physicians, and may fix the terms of their office. In any county in which the coroner or any of the coroners is not a physician duly licensed to practice medicine in this state, the board shall appoint one or more coroner's physicians. Each coroner's physician appointed pursuant to this subdivision shall by virtue of his office be a deputy coroner and shall possess the powers and perform the duties of the coroner, during the absence or inability of the coroner to act, or in the event of a vacancy in the office of coroner. 5. Certificate of election or appointment. Upon filing in the office of the county clerk a certificate of election or appointment of any officer, together with the oath of office and official undertaking prescribed by law, the county clerk shall execute and deliver to such officer a certificate stating that he or she has duly qualified and is entitled to assume the duties of his or her office. On or before the tenth day of January in each year and thereafter within five days after any subsequent appointment is made, the clerk of the board of supervisors shall file in the office of the county clerk a certificate showing the names of all officers of the county appointed by the board and the amount of the official undertaking, if any, required in each case. On or before the fifteenth day of January in each year and thereafter within five days after any person is elected or appointed to any office within the county, the county clerk shall file in the office of the executive department of the state a certificate showing the name of each person so elected or appointed who has duly qualified and, within the same time periods, file the name of any person appointed to the office of director of real property tax services with the commissioner of taxation and finance. 6. Notice of vacancy in office. Within ten days after any vacancy occurs as prescribed by section thirty of the public officers law, the county clerk shall give notice thereof to the governor when the power of appointment is vested in the governor and to the board of supervisors when the power of appointment is vested in said board. 7. Filling of vacancies. Except as hereinafter provided, a vacancy in an elective county office, shall be filled by the governor by appointment and for the office of sheriff with the advice and consent of the senate if in session. When a vacancy shall occur, otherwise than by expiration of term in the office of county judge, surrogate, or judge of the family court, it shall be filled for a full term at the next general election held not less than three months after such vacancy occurs and, until the vacancy shall be so filled, the governor by and with the advice and consent of the senate, if the senate shall be in session, or, if the senate not be in session, the governor may fill such vacancy by an appointment which shall continue until and including the last day of December next after the election at which the vacancy shall be filled. A vacancy in the office of coroner shall be filled by the board of supervisors. Such officer shall hold office until and including the thirty-first day of December succeeding the first annual election at which the vacancy can be filled by election. A person appointed to fill a vacancy in an office named in the constitution shall receive the same compensation that was fixed for the office for the most recent elective term. The board of supervisors shall fill any vacancy in an appointive county office for the unexpired term as prescribed by law.