Yes, Wisconsin imposes fines on dog owners whose dogs cause damage. These fines are paid to the court, though, not to the victim. These penalties are outlined in Section 2 of Wisconsin Statute 174.02:
(2) PENALTIES IMPOSED ON OWNER OF DOG CAUSING DAMAGE. (a) Without notice. The owner of a dog shall forfeit not less than $50 nor more than $2,500 if the dog injures or causes injury to a person, domestic animal, property, deer, game birds or the nests or eggs of game birds. (b) After notice. The owner of a dog shall forfeit not less than $200 nor more than $5,000 if the dog injures or causes injury to a person, domestic animal, property, deer, game birds or the nests or eggs of game birds, and if the owner was notified or knew that the dog previously injured or caused injury to a person, domestic animal, property, deer, game birds or the nests or eggs of game birds. (c) Penalties in addition to liability for damages. The penalties in this subsection are in addition to any other liability imposed on the owner of a dog.
It's not uncommon for a dog owner with a dog that has a history of causing damage to want to avoid any involvement with the courts or the police. If the injury you suffered is serious, we don’t recommend going along with any settlement proposal that stipulates you won’t file a police report.
Get the medical treatment you need, then file a report with your police department. If the dog has a history of unprovoked attacks, and the attack you suffered is serious, the dog needs to be euthanized before it attacks someone else. Wisconsin Statute 174.02 includes provisions for this.