Most species of wildlife in Illinois are protected by the Illinois Wildlife Code. Most mammals cannot be legally trapped unless the Illinois Department of Natural Resources issues a permit.
It is not true that raccoons have to be euthanized. By law, raccoons in Illinois must either be: 1) released on the same property within 100 yards of where the animal was captured, 2) surrendered to a licensed veterinarian who is a licensed wildlife rehabilitator, or 3) humanely euthanized. The biologist issuing the permit will determine the appropriate outcome for each case.
Also, homeowners associations must request a permit from the IDNR each time they plan to trap. I've contacted the IDNR district wildlife biologists in Cook County about your questions. They are Bob Massey and Joe Rogus, and they can be reached at (815) 476-0256. If you call them, Mr. Massey told me that they can help direct you to the appropriate Illinois Conservation Police Officer.