Question: If I live in Vermont and work in Massachusetts, would I have to pay Vermont income tax, Massachusetts income tax or

both?
A New Hampshire job is one thing, since there is no income tax there. But both Vermont and Massachusetts, I think, have income taxes.
Is there some agreement between Vermont and Massachusetts so that someone who worked in one state and lived in the other only paid state income tax to one state? Or so that the person paid a fraction of each state's tax, so that there was not a doubled tax burden? I can't imagine being expected to pay full income tax to two states.