No. You pay tax to the state in which you live, or sometimes you pay tax in two states if if lived in one state and earned income in another state. The fact that the annuity is "from" WI does not make it taxable in WI if you have lived in IL all year. IL does not tax retirement income.
**Disclaimer: Every effort has been made to offer the most correct information possible. The poster disclaims any legal responsibility for the accuracy of the information that is contained in this post.**