Report the attack to the authorities.
The hospital will send the bite incident to the Department of Health for the rabies check and quarantine of the dog. They do not pass on any information to the authorities. That is left to your discretion. While it is a personal decision, it is encouraged to report the attack to the police. If a dog has attacked you or a loved one, it may do so again to someone else. There should be a paper trail on the dog. While it may be a sensitive issue if you know the dog owner or are even related to them, it's best to take the emotion out of the equation and calmly explain your reasons about wanting safety first. If they are responsible dog owners, they should agree.
If the attack was serious, request an investigation.
While the police report is important, if you feel the attack was serious enough, request and investigation. Attacked is defined as "The deliberate action of a dog, whether or not in response to a command by its owner to bite, to seize with its teeth or to pursue any human or domestic animal."
If this was a severe dog bite or an attack, the authorities should investigate. This person, whether they are the police, animal control officer or a dog warden, should be able to cite the owner and have the authority to testify and prosecute in court, should it come to that. They should get your statement, statements from the dog owner, and any others who witnessed the attack. If there are past attacks that you know about, see if the investigator can get statements from them too. Again, it is advisable to make sure whoever is launching the investigation is able and willing to cite the dog owner if they determine that is warranted.
Sometimes the police will go out to investigate after you file the report right away. Other times, it will be the dog warden, or animal control officer. The important thing is one of them goes out to get a statement from you, the dog owner, any other witnesses and investigate the incident. Whether the attack happened to you, a loved one, or a pet, it is their duty to take your attack seriously and swiftly take action.
If the incident doesn't in your mind warrant as an attack, nor did not cause severe injury, you may not need to contact the dog warden if you've filed a report with the police already.