This irregularity in the boundary is the result of territorial disputes in the late 1600s , culminating with New York giving up its claim to this area , whose residents considered themselves part of Connecticut , in exchange for an equivalent area extending northwards from Ridgefield , Connecticut to the Massachusetts border as well as undisputed claim to Rye , New York . This irregularity in the boundary is the result of territorial disputes in the late 17th century , culminating with New York giving up its claim to the area , whose residents considered themselves part of Connecticut , in exchange for an equivalent area extending northwards from Ridgefield to the Massachusetts border as well as undisputed claim to Rye , New York .