Each state is different. I assume you were once a resident of the state to get a driver's license.
Four states make ending your residency very difficult: California, New Mexico, South Carolina, and Virginia.
Usually, the determining factor is whether you have income in that state. In Virginia, even a little income requires you to file as a non-resident. You are required to report your total income there, both in state and out of state.
If you can get through to a state revenue person, a lot of times this can be cleared up over the phone. That has happened to me twice. After a brief conversation, I was told not to file.