According to a 1650 agreement with the Dutch , the western boundary of Connecticut ran north from the west side of Greenwich Bay `` provided the said line come not within 10 miles ( 16 km ) of Hudson River . '' According to the Hartford Treaty with the Dutch , signed on September 19 , 1650 , but never ratified by the British , the western boundary of Connecticut ran north from Greenwich Bay for a distance of 20 miles `` provided the said line come not within 10 m ( 16 km ) of Hudson River .