Your resident state of VT will tax you on all your income you earn regardless of where earned.

NH has no income tax so no return is need to for NH.

If you would have happened to work in a state with income tax (outside of VT) you would file a nonresident return for that state, and then VT would give you a credit for taxes paid to that state as VT would also tax it.  This will prevent two states from taxing same amount.