My nephew is in almost same situation. I am doing his taxes, but I never saw a W-2 with two states (WI & IL). The problem is my nephew moved to IL in April of 2018; therefore, he never worked in WI. He never notified his employer that he was living in IL so they deducted taxes in both states. Now when I try to do his income tax it says that he owe over $700 in IL, and since WI doesn't have all their forms ready I cannot figure out the other state. But now this reciprocal agreement states that he is supposed to pay taxes only in the state he lives (which is IL) because he should of NOT pay taxes in WI, but he did!
