As always...lots of ideas and assumptions....but Fisherman is correct. MNR state that if you want to keep the black bear, woodland caribou, white-tailed deer, American elk, or moose, YOU SHALL report the acquisition immediately to the nearest MNR office. This can be as simple as calling the MNR and letting them know the details and where the animal is being kept. If a CO wants to come and inspect it, they might and you are then covered. If you don't want the deer and it is dead and not suffering, you can just leave it in the ditch. Usually someone else will come along shortly and claim it...or as stated a few times...Call another OFNer.
As for Police. They cannot give you permission to have the deer, etc... even though they sometimes think they can. Always call the MNR and get the permit of reporting! You might need the Police though for the accident report if damage was done!
Cheers!