You get the same six-month extension to file and pay Maryland income tax that the IRS gives for service in a designated combat zone or qualified hazardous duty area. Your spouse gets the extension too.
There is nothing to apply for in advance. Write the name of the combat zone or hazardous duty area on your Maryland return when you file, and contact the Comptroller of Maryland if you are contacted about a late filing.
Your orders or Leave and Earnings Statements showing service in the designated area and the dates.