As TomD8 mentions, Massachusetts does tax income you earned in Massachusetts. If you were living in a state that also has a state income tax, that state would give you a credit on their tax return for the amount of tax liability you have in Massachusetts. But, since you live in NH, a state without its own state income tax, they will not provide you with such a credit. Instead, you will file a Massachusetts Non-Resident tax return. You may get some refund of income tax when you do, but it is very unlikely that you will be fully refunded all of the MA withheld tax.
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