Which entity oversees the administration of municipal court in Texas?

The Texas Judicial Council is the correct answer because it is the entity responsible for overseeing the administration of the judicial system in Texas, including municipal courts. The Council focuses on the improvement of the state's judicial system and provides a centralized authority to address issues related to court operations, judicial policies, and efficiency. It plays a fundamental role in ensuring that municipal courts operate smoothly and adhere to the relevant legal framework, thereby enhancing the overall functionality of the court system at various levels, including municipal courts.

The other options don’t directly relate to the administration of municipal courts. The Court of Appeals handles appeals from lower courts but does not oversee the day-to-day administration of municipal courts. The County Court functions as a trial court but has a different scope and does not supervise municipal courts. The Department of Public Safety is primarily concerned with public safety and law enforcement and does not have jurisdiction over court administration matters. Therefore, the Texas Judicial Council is clearly identified as the correct governing body for municipal court administration in Texas.