New York City Courts
|New York State Unified Court System|
The New York City court system consists of civil, criminal, and family courts. All have a presence in each borough and have city-wide jurisdiction. New York City courts have jurisdiction in the five counties that are coterminous with the five boroughs, but in practice most cases are handled in their own county/borough. Unlike the rest of New York State, New York City does not have typical County Courts.
Civil Court 
The New York City Civil Court is the civil branch of the New York City courts system. The court handles all small claims cases (up to $5,000) and all civil cases within the five counties of New York City with a monetary value up to $25,000, as well as residential and commercial landlord-tenant disputes and certain cases transferred from the Supreme Court. Generally speaking the court does not have any equitable jurisdiction but can award money damages or possession of property only. There is a branch of the civil court in each of the five boroughs.
Judges of the Civil Court are elected to 10-year terms in either borough wide or district elections. The Civil Court districts are parts of the boroughs and do not cross borough lines. Party leaders frequently designate candidates for the Civil Court judgeships who then face an open primary against others who qualify for the ballot. The party machine usually manages to elect most of its judicial candidates. Vacancies on the Civil Court are filled by mayoral appointment.
Civil Court Judges can be designated to sit in the city's Criminal Court or as Acting Justices of the New York State Supreme Court. In addition, Civil Court Judges can be assigned to a borough they were not elected in, but they have to live in the borough or district where elected.
Criminal Court 
The New York City Criminal Court is the beginning level trial court of criminal cases in the City of New York. The court handles arraignments, misdemeanors, and minor felony cases. Criminal motions are also handled in this court, along with some jury trials. Major felony cases are referred to the New York State Supreme Court. Judges of the Criminal Court are appointed by the Mayor of New York to a 10 year term. Several Criminal Court Judges are designated as Acting Justices of the New York State Supreme Court. In addition, Judges of the New York City Civil Court are designated to sit in the Criminal Court.
Traffic violations in New York City are handled in the Traffic Violations Bureau, which operates under the New York State Department of Motor Vehicles. The Bureau is an administrative law agency and not a judicial tribunal.
Family Court 
The New York City Family Court hears matters involving children and families. Its jurisdiction includes custody and visitation, support, concurrent jurisdiction with Criminal Court for family offenses (domestic violence), persons in need of supervision, delinquency, child protective proceedings (abuse and neglect), foster care approval and review, termination of parental rights, adoption and guardianship. Judges of the Family Court are appointed by the Mayor to 10 year terms.
Family Court does not have jurisdiction over divorces, which must be litigated in the Supreme Court. Further, although Criminal Court domestic violence parts typically hear all cases involving crimes against intimate partners (whether opposite- or same-sex), New York law defines family offenses to include only those related by blood, actual marriage (common law marriage is not recognized in New York), or a child in common.
Justice Jane Bolin became the first black female judge in the United States when Mayor Fiorello La Guardia swore her in to the bench of the Family Court, then called the Domestic Relations Court, in 1939. Her 10-year appointment was renewed by the city's mayors three times until she reached the mandatory retirement age of 70.
Supreme Court of the State of New York 
Like all other counties in the state of New York, every county in New York City has a sitting Supreme Court of the State of New York. In New York State, the Supreme Court is the state's trial court of original and unlimited jurisdiction. Normally, the Supreme Court only hears cases that are outside of another court's subject-matter jurisdiction.
In New York City, the Supreme Court handles criminal cases on indictment; elsewhere in New York, the County Court hears these cases. As in the rest of the state, the Supreme Court also handles larger civil cases.
Other courts 
The Midtown Community Court in Manhattan opened in 1993 as a project of the Center for Court Innovation. It hears "quality-of-life" criminal cases, with a view toward rehabilitation instead of punishment. For example, judges may order offenders to perform community service and refer them to such social services as drug treatment, mental health counseling, and job training.
The Red Hook Community Justice Center in Brooklyn opened in 2000 as the nation's first multi-jurisdictional community court. Built to alleviate the chronic lack of access to justice services in the isolated area of Red Hook, Brooklyn, the court combines family, civil, housing, and minor criminal court functions and takes a community development approach to justice through such programs as the Youth Court, where teenagers are trained and act as mediators to help their peers resolve disputes.
Further reading 
Galie, Peter J. and Bopst, Christopher, The New York State Constitution (2nd ed. 2012)
Lincoln, Charles Z., The Constitutional History of New York from the Beginning of the Colonial Period to the Year 1905 (1906)
State of New York, Department of State, New York Constitution 
The Historical Society of the Courts of the State of New York 
- nycourts.gov Official history of the Civil Court