The Connecticut Irish American Historical Society (CTIAHS) was founded in 1988 and is the main ethnic Irish historical and genealogy group in the state. The activities of the groups are wide-ranging and include the publication of a newsletter, a genealogy group, a library/archive, oral history interviews with older members of the community, and participation in festivals and ceremonies. Based in East Haven, just across the Quinnipiac river from New Haven, the group has over 300 members and is involved in pretty much everything to do with Irish heritage in Connecticut.
CTIAHS has a dedicated genealogy group that meets once a month. They have published books such as Early New Haven Irish and Their Final Resting Places: The Old Catholic and Saint Bernard Cemeteries and have made a valuable contribution to the study of Irish genealogy in Connecticut.
You can learn all about the organization on their website, here.
 Bohan, Ellen, Patricia Heslin, Paul Keroack, Bernard Singer, Rosanne Singer, eds. with Neil Hogan, Robert O. Larkin, and Jamie Longley. Early New Haven Irish and Their Final Resting Places: The Old Catholic and Saint Bernard Cemeteries. Hamden, CT: Connecticut Irish American Historical Society. 2013.