The Croton River is a river in southern New York with three principal tributaries: the West Branch, Middle Branch, and East Branch. Their waters, all part of the New York City water supply system, join downstream from the Croton Falls Reservoir. Together, their waters and the reservoirs linked to them represent the northern half of the New York City water …The Croton River is a river in southern New York with three principal tributaries: the West Branch, Middle Branch, and East Branch. Their waters, all part of the New York City water supply system, join downstream from the Croton Falls Reservoir. Together, their waters and the reservoirs linked to them represent the northern half of the New York City water system's Croton Watershed.