Heres where you can find the information
http://dnr.state.il.us/DOO/pdfs/CrossbowPermitApp.pdf
Heres the first paragraph of the application:
For the purpose of securing authorization to hunt with a crossbow, I attest that I have a permanent physical impairment due to injury or disease, congenital or acquired, which renders me so disabled as to be unable to use a conventional bow and arrow device.