It depends on which states you are asking about*. The general rule is: your report
all your income on your home state tax return, even the income earned out of state.
You file a non-resident state return for the state you worked in and pay tax to
that state. Your home state will give you a credit, or partial credit, for what
you paid the non-resident state.
So, do withholding for the state you are working in.
*Some states have reciprocal agreements; in which case you would withhold for your permanent residence state.
