Which type of court has jurisdiction over minor criminal offenses not involving confinement?

Justice Courts have jurisdiction over minor criminal offenses that typically do not involve confinement, such as misdemeanors that carry smaller penalties. These courts handle cases such as minor traffic violations, certain low-level criminal offenses, and other civil matters. Their role is significant because they provide a local venue for resolving disputes and addressing minor criminal issues promptly.

While County Courts and Municipal Courts also have their own specific jurisdictions, Justice Courts are uniquely positioned to handle minor offenses across various geographic locations, aligning with their local community focus. District Courts, on the other hand, generally deal with felony cases and more serious criminal matters, making them unsuitable for the specified scope of this question. Thus, Justice Courts are specifically designed to address minor criminal offenses, which is why they are the correct answer.