Utah starts from your federal adjusted gross income, so military pay that federal law does not tax is also not taxed by Utah. That includes pay you earn in a combat zone and hazardous duty pay.
There is nothing to apply for. Pay that is excluded from your federal return is already outside your Utah taxable income, so file your Utah return from your federal adjusted gross income as normal.
Your Leave and Earnings Statements or orders showing the combat zone or hazardous duty service, kept with your tax records.