Get Your Dog Care Questions Answered by Experts
It can be given either way depending on what the product is that is used to do this.
From this site
"Rabies vaccine is to be given according to the vaccine manufacturers recommendation, either subcutaneously or in a muscle. The vaccine should be delivered by a veterinarian or under the direct supervision of a veterinarian."
If the owner gives it then its not considered valid should the dog bite anyone or another animal, or be attacked or bitten by another animal.
Hope this helps you!