This happened to my sister in NY and FL. She moved to FL from NY but paid NY taxes all year.

She submitted an affidavit and proof of FL residency since the date of claim on the refund request. Then she was audited but had all her ducks in a row and no issues.

Basically, just make sure you are listed by your company as NH Remote and not MA, and have proof you lived in NH and you should be set. Might just be a lengthy process.