The person who is driving the vehicle that hits the big game animal is the only one who can obtain a salvage permit for road kill. This person can then make a gift of the animal if he or she so chooses.
As was stated above california does not allow for the retrieval of roadkill. Many states do allow it with a written approval or Tag. only a few allow the removal with out approval
Another thing that you may think about is that while many people are honest, there are also a fair number of people who would use there vehicle as a weapon if given the opportunity. Hell I know an idiot here in florida that runs deer down in an airboat so that he does not have to waste a bullet.