Nebraska does not tax military retired pay. Any military retirement included in your federal gross income is exempt from Nebraska income tax. Thrift Savings Plan distributions taken after you retire are also not subject to Nebraska tax, though early distributions can be taxed more heavily.
There is nothing to apply for. Subtract your military retirement from the income you report on your Nebraska return. If Nebraska 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.