Depending on what city you live in, there are ordinances that prohibit allowing your dog to “run at large.” This varies depending on the city, but they all say generally the same thing.
In short, a Dog at Large ordinance imposes a duty upon owners of dogs to refrain from allowing their dog to “run at large” within the city limits. This restriction generally does not prohibit the appearance of any dog upon streets or public property when the dog is under restraint and kept under the control of the person charged with its care. A dog is not considered “at large” if it is kept within the property limits of its owner.
The penalty for a violation of this ordinance is typically a misdemeanor and can be settled by paying a fine out of court or appearing in court and resolving there.
There is also a Minnesota state statute which outlines the violation of Public Nuisance and is a Misdemeanor. Minnesota Statute § 347.04 states that “any dog that habitually worries, chases, or molests teams or persons traveling peaceably on the public road is a public nuisance.” Meaning it is a criminal offense and requires a court appearance in front of a judge.