A Consolidated city-township refers to any city or municipality which has been consolidated with the government of a civil township.
New York
Five towns are coterminous with their single village: Green Island in Albany County; East Rochester in Monroe County; and Scarsdale, Harrison and Mount Kisco in Westchester County. When such an entity is formed, officials from either unit of government may serve in both village and town governments simultaneously. A referendum is held to decide whether residents prefer a village-style or town-style government, which will then function primarily as a village or town but will perform some of the functions of the other form.
References
Consolidated city-township Wikipedia(Text) CC BY-SA