You can file criminal charges against the abuser for acts of domestic violence, because they are all crimes. Criminal charges can only be filed at the local police department, and they will usually be heard at the local municipal court.
For very serious crimes, the county prosecutor may take your case to state criminal court. You do not have to file criminal charges, but the law does allow you to file them if you choose, even if you also get a restraining order. You have a year after any incident to file criminal charges. The police can also file charges on their own and must do so when you show signs of injury or if a weapon was used. If the abuser is found guilty of the criminal charges, the court can impose fines, probation, or even jail as punishment.