Ind. Code § 20-26-4-4

Sec. 4. If a vacancy in the membership of a governing body occurs for any reason (including the failure of a sufficient number of petitions for candidates for governing body membership being filed for an election and whether the vacancy was of an elected or appointed member), the remaining members of the governing body shall by majority vote fill the vacancy by appointing a person from within the boundaries of the school corporation, with the residence and other qualifications provided for a regularly elected or appointed board member filling the membership, to serve for the term or the balance of the term. However, this subsection does not apply to a vacancy:

(1) of a member who serves on a governing body in an ex officio capacity; or

(2) a vacancy in an appointed board membership if a plan, resolution, or law under which the school corporation operates specifically provides for filling vacancies by the appointing authority.