(A) A county treasurer may appoint an employee in his office to be his deputy. The appointment must be filed with the State Treasurer and the governing body of that county. When the appointment is filed, the deputy may act for and on behalf of the county treasurer when the treasurer is incapacitated by reason of a physical or mental disability or during a temporary absence.

(B) If there is a vacancy in the office of county treasurer by reason of death, resignation, or disqualification, the appointed deputy shall carry out the duties of the office until a successor is appointed or elected and qualified.