Here are links to some Connecticut labor organizations.  A more extensive list is available at the AFL-CIO, Connecticut link.  International Unions are described on the website that  links to Unions Affiliated with the AFL-CIO.

AFL-CIO, Connecticut

AFSCME Council 4

AFT Connecticut

American Postal Workers Union Local 147

Connecticut Central Labor Councils

Connecticut Working Families - Affiliates

Connecticut United Labor Agency

International Association of Machinists and Aerospce Workers, District 26

 International Association of Machinists and Aerospace Workers,Local Lodge 743

International Association of Machinists and Aerospace Workers, Local Lodge 1746

New England Health Care Employees Union - 1199NE/SEIU

 United Food and Commercial Workers Local 371

United Food and Commercial Workers Local 919