What branch of government do the courts belong to?
Judiciary
In many jurisdictions the judicial branch has the power to change laws through the process of judicial review. Courts with judicial review power may annul the laws and rules of the state when it finds them incompatible with a higher norm, such as primary legislation, the provisions of the constitution or international law. Judges constitute a critical force for interpretation and implementation of a constitution, thus de facto in common law countries creating the body of constitutional law. For a people to establish and keep the 'Rule of Law' as the operative norm in social constructs great care must be taken in the election or appointment of unbiased and thoughtful legal scholars whose loyalty to an oath of office is without reproach. If law is to govern and find acceptance generally courts must exercise fidelity to justice which means affording those subject to its jurisdictional scope the greatest presumption of inherent cultural relevance within this framework.
Constables in the United States
While Constables primarily serve the Courts, they belong to the executive branch of government.