Constables in the United States
While Constables primarily serve the Courts, they belong to the executive branch of government.
Judiciary of New York (state)
The New York State County Court operates in each county except for the five counties of New York City (in those counties, the Civil Court, Criminal Court and Supreme Court operate in place of a typical County Court). In many counties, this court primarily hears criminal cases (whereas the Supreme Court primarily hears civil cases), and usually only felonies as lesser crimes are handled by local courts.
There are numerous administrative courts which are not considered part of the judicial branch of government.Decisions of the New York Court of Appeals are binding authority on all other courts, and persuasive authority for itself in later cases. Decisions of the New York Supreme Court, Appellate Division department panels are binding on the lower courts in that department, and also on lower courts in other departments unless there is contrary authority from the Appellate Division of that department. Decisions by the Supreme Court, Appellate Term must be followed by courts whose appeals lie to it. Published trial court decisions are persuasive authority for all other courts in the state.