Unless otherwise provided by law, vacancies arising in appointive and elective offices of the municipality shall be filled by appointment by the Mayor for the remainder of the unexpired term, provided that:
(A) Vacancies in the office of the Mayor shall be filled in the manner provided by § 31.17;
(B) Vacancies in the membership of the Legislative Authority shall be filled in the manner provided by § 32.06;
(C) Vacancies in the office of President Pro Tempore of the Legislative Authority shall be filled in the manner provided by § 32.03;
(D) Vacancies in the office of Clerk or Treasurer may be filled in the following manner: The Mayor may appoint a person to serve as acting officer to perform the duties of the office until a permanent officer is appointed to fill the vacancy.
(R.C. § 733.31(A))