Ind. Code § 5-8-4-1
Whenever any officer, servant or employee of the state of Indiana, or of any board, bureau, commission, department, division, instrumentality or agency thereof, or of any city, town, county, township, or school corporation, or of any board, bureau, commission, department, division, instrumentality or agency of any city, town, county, township, or school corporation, shall submit in writing his or her resignation, whether to take effect at once, when accepted, or at some future fixed date, with the proper officer, person or persons or authority of government to receive such resignation, the person so submitting such written resignation shall have no right to withdraw, rescind, annul or amend such resignation without the consent of the officer, person or persons or authority of government having power by law to fill such vacancy.
IC 5-8-4-1