Constables in the United States
While Constables primarily serve the Courts, they belong to the executive branch of government.
Constitution
Constitutions usually explicitly divide power between various branches of government. The standard model, described by the Baron de Montesquieu, involves three branches of government: executive, legislative and judicial. Some constitutions include additional branches, such as an auditory branch. Constitutions vary extensively as to the degree of separation of powers between these branches.