One shouldn’t be allowed to be registered to vote in two different places. I am completely fine with out of state college students voting in New Hampshire, but not if they are also registered in some other state.
Q: I have registered or previously voted in another state. Can I vote in New Hampshire?
A: If you’ve register or voted in another state in the past but live at school in New Hampshire, you can register and cast your ballot here. You may only vote in one state, of course.
If you’re trying to get in-state tuition rates, seems to me it’ll be easy to find out just who was registered where, at least when it comes to students. Any offenders there will be easy to nail. It’s the non-students bussed in that’ll take more time to find.