Good afternoon, Determining if you have a nuisance wildlife situation is taken on a case by case basis. Without knowing the specifics of the deer situation you are dealing with, I can only provide general guidelines.
If the animal(s) is causing substantial property damage or is a threat to public health or safety, those would typically be considered nuisance cases. The Illinois Department of Natural Resources District Wildlife Biologist assigned to your county makes the determination if the situation warrants removal of the animal(s).
Deer nuisance issues are handled differently than other wildlife nuisance cases. You would not call a Nuisance Wildlife Control Operator for deer removal. If you live within a municipality you should call the municipality first. Municipalities may be issued Deer Population Control Permits by the Illinois Department of Natural Resources which authorizes the municipality to control the deer population in the area. If you live outside of town, you may be eligible to receive a Deer Removal Permit which would be issued by the District Wildlife Biologist. This page of the website can help you determine what type of assistance is available: http://web.extension.uiuc.edu/wildlife/permit_deer.cfm#individual
If you have further questions please feel free to e-mail me at lasimmon@illinois.edu.