If you file a tax return in a state, and then you leave. Make sure you file a tax return the next year as well but put down zero taxable income.
What I have seen states do, is take the last year you filed a return "presume" you made that much in the next year but just "forgot" to file, and then charge you for back taxes. You counter this behavior by filing a $0 tax return so that the last year on the books you made $0 and when they use the last year you filed to compute your 'expected' return for the current year they will start with $0. A CPA friend suggested that you continue this for three years as that was the 'average' over which they might make a computation.
Either way, its a pain. But filing a state return with $0 on it is pretty straight forward thing these days with efiling.