In most jurisidictions, a dog must be under the control of the owner at all times. Many further specify that a dog must be leashed. Unless you left the highway, or hit a dog being walked by its owner in a crosswalk, the liability would most likely rest with the owner who had lost control of the dog.
In some jurisdictions, you are required to notify the Police or Animal control, or you may be cited for leaving the scene. It's also a good idea to go to the nearest house in a neighborhood area and ask if they know to whom the animal belongs. Don't leave a dog in the street if it just seems to be in shock or slightly injured. You may be leaving it to be re-injured by the next passing vehicle. If you can move the animal safely to the verge, out of harms way, please do so. Safety first for yourself. Injured dogs frequently bite. I keep a little thin rope and an old rug in my trunk, just in case. you can firmly but gently pass the rope 3x around the muzzle. Scooch the dog onto the rug as gently as possible. MOve to a safe area or transport to vet or Shelter if possible and you arefeeling humane.