You get an automatic 60 day extension to file your Indiana income taxes while you are serving outside the United States and Puerto Rico. If you are assigned to a combat zone, you have 180 days after you redeploy to file.
There is nothing to apply for in advance. File your Indiana return within the extended window and keep your orders on hand in case the Department of Revenue asks why the return is late.
Your orders showing the overseas assignment or combat zone service, and your redeployment date.