As others have stated 100% illegal to use a gun to finish off a deer. The only legal way would be if you were in fear of your life but if the deer is down there is no way that would fly (you'd also have to contact law enforcement ASAP).
As it relates to a deer hit but a car it's also mostly illegal to put down the deer. The only exception I could think of is if it was during firearm season and the deer made it off of the right of way onto your property, you have permission from the land owner or state land that allows hunting. In this case you'd have to use your tag as well.