You will need to file a Massachusetts non-resident return claiming the taxes paid. Then you will file your New Hampshire return and claim a credit for taxes paid to another state. This will give you credit for the taxes paid to Massachusetts. To complete in TurboTax, make sure you start your non-resident return first. The credit for taxes paid to another state will be included when you complete the New Hampshire return.
For more information, see the link below:
Multiple State Returns
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