Ind. Code § 15-12-1-23

Sec. 23. When a vacancy on the board of directors occurs, other than by expiration of term of office, the remaining members of the board may fill the vacancy by a majority vote of the remaining members, unless the bylaws provide for the election of directors by districts. If the bylaws provide for the election of directors by districts, the board of directors may call a special meeting of the members in that district to fill the vacancy or may fill the vacancy as in the case of any other vacancy. A director who is elected or appointed by the board of directors to fill a vacancy on the board shall serve until the next annual or special meeting of the members.