For tax purposes definitely look up the fine print in the state codes for yourself. That said, a lot of states (you know, the five or something I've looked at... so, uh, a few) define resident as where you have your domicile, where you intend to come back if you go on trips, etc, except they say it less simply of course. So you can make an argument both ways possibly.
If you move to a new state and you have the forms they require as proofs of residency, switch your license, your car, and your voter registration, and pay taxes in the new state if it works better for you. Some states might make it harder (VA i seem to recall) to become a resident but for others it is pretty simple.
Whether you're allowed to remain a resident of your old state I dunno - as a grad student in an institution of higher learning i stayed in my old state as a dependent, then for a couple of years as an independent still paying to my old state. I could claim I was only here for school, my only tie was to school, and my intent to return was to my old state vs stay here (which is the argument they use on their side in not giving me in state tuition). I think you can typically do that but check the fine print. I've now switched to the state I go to school in (but like you wouldnt necessarily get instate tuition here because i'm in school).
Only thing then is you might have to file two state tax forms. Your income in your new state may be taxed by your new state, so you'll fill out forms as a nonresident there, and your home state tax form will be as a resident who earned income out of state, and your home state should apply what taxes you've already been charged by newstate against the balance that homestate wants from you. So that can be kind of a pain if both states have income tax.
Hopefully marginally clearer than mud.