Since your employer withheld and made the payments to your former state, you will need to file a nonresident return for your former state. You will enter your W-2 as is, but then as you walk through the nonresident state section, you will adjust the income to $0 for the state and leave the amount withheld as whatever is showing they withheld. Doing this, you will receive a full refund for the taxes paid to the wrong state.
You will then need to file your Montana state return as a resident. Since nothing was withheld by your employer, you will likely need to pay Montana the amount that is due. Montana, as most states do, does have a late payment penalty for not paying as you go with your taxes. However, they also have an automatic late payment waiver of penalty if this is your first time and if you pay 90% of your tax liability by the due date of your return. If this is not your first time, or you do not for some reason receive the penalty waiver, you can contact the Montana Department of Revenue for assistance in possibly reducing your penalty.
You will likely need to go through a similar process for next year if you did not update your address with your employer prior to your first paycheck of the year. You should update this asap if you haven't already done so. Once your address is updated you should double check on your pay stubs to see which state they are withholding taxes for.
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