there's a reciprocal agreement between Illinois and Wisconsin. you only pay taxes in your resident state. This means that both you need to amend both Illinois and Wisconsin.
in Wisconsin you report no wages and indicate you are an Illinois resident so you should respond to Wisconsin with a statement that you were an Illinois resident for the entire year and include a copy of the amended Wi return . In Illinois you can't claim any credit for taxes paid to Wisconsin.
since you work in Wisconsin and are a resident of Illinois, Indiana, Kentucky, or Michigan, submit exemption Form W-220 to your employer and make sure Illinois withholding starts.
from IL-1040 instructions
an Illinois resident who worked in Iowa, Kentucky, Michigan, or Wisconsin, you must file
Form IL-1040 and include as Illinois income any compensation you received from an employer in these
states. Compensation paid to Illinois residents working in these states is taxed by Illinois. Based on
reciprocal agreements between Illinois and these states, these states do not tax the compensation of
If your employer in any of these states withheld that state’s tax from your compensation, you may file the
correct form with that state to claim a refund. You may not use tax withheld by an employer for these
states as a credit on your Illinois return.
1. If you paid IL income tax on 100% of your income (including your earnings from WI), and you did NOT take any Other State Credit on your IL return, then there is no need to amend your IL return.
2. You should respond to the letter from WI by explaining that you are a full-year resident of Illinois and thus you do not owe WI taxes on your W-2 income. This may result in WI correcting the situation without your needing to file a WI tax return.
3. If your WI employer is still withholding WI taxes, you should do as @Anonymous stated and file WI Form W-220 with your WI employer. Here's a link to that form: