Rhode Island does not tax military retired pay. Your military pension is exempt from Rhode Island personal income tax. Thrift Savings Plan money is different: TSP does not withhold state or local tax, but all TSP distributions are subject to state tax and early distributions can be taxed more heavily.
There is nothing to apply for. Leave your military retired pay out of the income you report on your Rhode Island return. If Rhode Island tax was withheld from it by mistake, file a return to claim the refund.
Your Form 1099-R showing the retired pay, kept with your tax records.
