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 R.C. § 733.25, or a substantially similar municipal ordinance;
(B) Vacancies in the membership of the legislative authority shall be filled in the manner provided by R.C. § 731.43, or a substantially similar municipal ordinance;
(C) Vacancies in the office of President Pro Tem of the legislative authority shall be filled in the manner provided by R.C. § 731.11, or a substantially similar municipal ordinance;
(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)) (2000 Code, § 30.07)