Vermont was originally inhabited by Native American tribes of the Algonquian and Iroquois nations. Most Native Americans belonged to the Algonquin nation tribe of Abenaki. Two of Vermont towns were names using Native words: Jamaica, from the Native word for beaver, and Winooski, from the Native word for wild onion place.
Native Americans were counted on the US federal census beginning in 1860. However, enumerators were ordered to only count those Native Americans who had renounced tribal rule, and therefor were considered American citizens. Native Americans who did not pay taxes were not counted. The 1870 US federal census lists Native Americans as "Indians" under the column of color.
Below are some resources where you can learn more about Native Americans in Vermont, including historical and genealogical information.
Ndakinna Cultural Center: Offers a "rotating" museum that travels throughout the state, educating people about the Abenaki tribe. See their schedule of events here.
Chimney Point Historic Site: Site of early Native American settlements. Located in Addison, Vermont.
Abenaki Nation Museum: Located in Swanton, Vermont, this museum educates people about the Abenaki community.
Koasek Traditional Band of the Koas Abenaki Nation: Information & events for this particular band of the Abenaki.
New England Native American Genealogy Mailing List: A mailing list for anyone with a genealogical or historical interest in Native Americans in the New England and New York areas. To subscribe send "subscribe" to firstname.lastname@example.org (mail mode) or email@example.com (digest mode).
Cyndi's List Native American Resources: This list of resources is not specific to Native Americans in Vermont, but is helpful to genealogists researching Native American lineage nonetheless.
Indian Health Service: Again, not specific to Vermont, but lists some wonderful resources for studying Native American genealogy.