@JH-HH --
The correct procedure is for you to file a non-resident KY tax return, allocating zero income to KY but showing the KY withholding, in order for you to obtain a refund of the incorrectly withheld KY taxes. ALL your income, including that on the 1099-R, should be allocated to your home state of Illinois. Illinois doesn't tax retirement income, but you still need to report the 1099-R on your tax return.
As others have said, the mailing address on your tax return should be whatever address you want the taxing authorities to use in case they need to contact you. Your state tax obligations are not determined by your mailing address.
If KY questions your return, explain the situation to them just as you explained it here.
The KY-IL reciprocity agreement does not apply to 1099-R income and thus is irrelevant to your situation.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
