If you discover that your pet has been hit by a car, approach with caution. Be sure you are safe from oncoming traffic and avoid being bitten by the injured animal. The pet should be safely removed from the roadway quickly and carefully so that you, your pet and approaching motorists are safe from further accidents. Once the pet is moved from the roadway, checked to see if it is breathing. If there is no breath or pulse, CPR can be performed.

Any injured animal should be muzzled for your own safety.

The only exceptions to this would be:dog-chasing-car:

An animal with chest injuries

Short nosed breeds (brachycephalic breeds like Pugs)

An animal that is vomiting

Pet owners need to try to remember that after a dog or cat has been hit by a car, its first instinct is to flee and to ignore pain. In nature this instinct protects animals from predators, but for domesticated animals it can cause more problems. Very carefully examine every part of your pet and watch for signs of labored breathing or pain response. It is important to take your pet to a veterinarian immediately after a car accident, even if the pet seems to be okay after the incident. Even if the pet is not obviously bleeding, the possibility that they have internal injuries is very high.

Source