Federal and state taxes are pay-as-you-go, so the deadlines are the quarterly deadlines for paying estimated taxes. So you would be subject to late penalties for each quarter.
Having said that, I'm not sure why you are having NC withhold taxes only to have them refunded to you; that would indicate the income is not NC sourced. If you did not physically work in NC you don't need to have NC taxes withhold but instead you need MT taxes withheld. You need to submit Montana form MW-4 (here) to your employer to have MT withhold. You will need to file the NC non-resident for 2023 to get a refund of any NC withholding so far in 2023.
If on the other hand if you actually worked in NC then NC should withhold because that is NC source income and you would claim a credit on your MT taxes for the taxes paid to another state thereby avoiding the late penalties because you are meeting the tax requirements of NC.
Here is a link to the MT Department Revenue discussion on the credit for taxes paid to another state.
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