Municipal courts will often deal with violations of the city laws that are committed within the city limits. Typically, these laws tend to deal with traffic offenses, shoplifting offenses, and minor offenses, which may even include dog leash violations. Yet, even though these courts are not state courts and often have limited jurisdiction, they are still able to solve most legal issues before escalating them to a higher level.
However, depending on the circumstances of your case, you may have a right to a jury trial to explain your side of the story in these Municipal Courts, and you may also be able to appeal a Municipal Court decision to the state level court.