Constables in the United States
While Constables primarily serve the Courts, they belong to the executive branch of government.
Government of New Jersey
The government of the State of New Jersey is separated into three distinct branches: legislative, executive, and judicial. The powers of the state are vested by the Constitution of New Jersey, enacted in 1947, in a bicameral state legislature (consisting of the General Assembly and Senate), the Governor, and the state courts, headed the New Jersey Supreme Court. The powers and duties of these branches are further defined by acts of the state legislature, including the creation of executive departments and courts inferior to the Supreme Court.
Like most states, the state allows the incorporation of county, and other local municipal government.