You may have to file two state tax returns.
You file a tax return with the state where you were physically present to earn the money, in this case, New Hampshire.
If New Hampshire is your state of residence the return you file is a New Hampshire Resident Tax Return. If your state of residence is elsewhere you file a New Hampshire Non-resident Tax Return.
If New Hampshire is not your state of residence then, you file a Resident Tax Return with whatever state you are a resident of.
You want to do the non-resident tax return first. Your state of residence taxes you on your world-wide income. You get a credit for taxes paid to another state on your resident tax return so you do no pay taxes twice on the same income.
You do the non-resident tax return first so that the credit flows properly to your resident state tax return.
