Yes, you will file the Illinois to receive a full refund because Wisconsin is a reciprocal state for Illinois. If you file both returns electronically and they are both accepted there is nothing else to do.
If you file the Illinois return by mail, attach a copy of the Wisconsin. You may owe some money to Wisconsin since there was Illinois withholding.
Do not try to use a "credit for taxes paid to another state" on the Wisconsin resident return, because you aren't paying any tax, you are requesting a full refund.
Which states have reciprocal agreements?
