Unfortunately IL... you may just have to call the wardens on me... i have continual problems with squirrels damaging my bird feeders year round. They eat the wood, plastic, etc... If they keep doing it, the will keep getting shot (or shot at generally).
Can you obtain a nuisance permit in your State ? I know some States grant permits if you can proove a loss or damage from wild animals.
I used to shoot squirrels and groundhogs everyday. The squirrels built a hotel in my attic, as well as a cafe, I believe. The groundhogs made tunnels under and around my pool that would put the Viet Cong's to shame and their holes were extremely hazardous to our multi-million dollar stock of Thoroughbreds and farm equipment.
Do it safely, if you HAVE to...But I wouldnt post it online if you're breaking the law....