Yes, you will need to file in both states. All investments are reported to your state of residence. In your case, that would be New Hampshire. TurboTax Online Deluxe or higher can file up to 5 states.
Be sure to enter the nonresident state, Massachusetts, first, when you start the state section. You may wish to notify your employer to withhold New Hampshire tax.
For more details, see How do I file a nonresident state return?
[Edited 02/01/2021 | 10:23 AM PST]
@jokon22
