New Hampshire imposes a 5% tax on interest and dividend income. If you do not have interest and dividend income income of more than $2,400 annually ( $4,800 for joint filers), then you are not subject to the interest and dividends tax, and do not have to file any New Hampshire return.
If you are not subject to the New Hampshire interest and dividends tax and would like to remove the return, you can delete your state return in TurboTax Online, as long as you haven't paid for it yet (or registered in a free version).
Please see the following TurboTax FAQ, "How do I delete my state return in TurboTax Online?":
You can then select Massachusetts in the state drop-down menu, in the State Taxes section, and proceed through the Massachusetts state interview section to complete a Massachusetts nonresident return..