The question cannot be answered, completely, until we know which states you are asking about, Which one do you live in which do you work in.
You also need to check with your employer if the will withhold for your home. So will tell you they only do work state.
That said:
Q. But are you still filling out a w-4 for the state you live in and getting both state taxes with held??
A. General rule: No. You only do the work state. The credit that your home state gives you will wipe out any tax on that income, so withholding is not necessary. But, for example, if the work state has a 2% tax rate and the home state 4%, the credit will not be enough. So, you either need to do withholding or make quarterly estimated payments.
