"The Treaty of Paris, which ended the American War of Independence, set the boundary at 'the northwesternmost head of the Connecticut River." However, three tributaries fed into the head of the Connecticut River, leaving each government setting the boundary with the tributary that gave it the most land." (Source: http://www.suite101.com/article.cfm/new_hampshire/46113)
For many years after the [American] Revolution, this Connecticut Lake region was claimed by both the United States and Canada. The settlers formed their own local government, and about 1829, the section became known as Indian Stream Territory [named after a small stream whose source is in the northern tip of the state]. On July 9,1832, the inhabitants organized the "Republic of Indian Stream," with a written constitution, council, assembly, and courts. The tiny State existed for three years...when after a dispute with the Canadian authorities the territory was occupied by New Hampshire Militia. Incorporated as Pittsburg in 1840, the north and west [boundary] lines were established in 1841, and by the Ashburton Treaty (1842) the region was awarded to New Hampshire [and the United States]. (Source :Ask Dr. Hearld- http://www.weirs.com/w_times/99archiv/02/11/askdr.htm)