Which type of court typically handles minor offenses and misdemeanors in New York?

The correct choice is Criminal Court, as this court specifically addresses cases involving misdemeanors and other minor offenses such as petty theft, low-level assault, and certain violations of state or local laws. In New York, Criminal Court is designed to handle less severe criminal matters, where the penalties may include fines or short-term incarceration rather than lengthy prison sentences.

Family Court focuses on matters relating to family law, such as child custody and support, and does not deal with criminal offenses. Claims Court is concerned with civil disputes, typically involving monetary claims and does not address criminal behavior. Traffic Court resolves violations of traffic laws, which is a specific subset of legal matters but does not encompass the broader category of misdemeanors that Criminal Court addresses. Thus, Criminal Court is the appropriate venue for handling minor offenses in New York.