I was reading through Geneabloggers's Civil War blogs list this morning, looking for new resources. In so doing, I stumbled across The USCT Chronicle (http://usctchronicle.blogspot.com/2011_01_01_archive.html). The USCT Chronicle offers genealogists and historians an introduction to the United States Colored Troops. These were units of African-American who served as part of the regular Union Army. If you know nothing about them, the blog is worthwhile reading.
Connecticut did not have a USCT regiment, but a Connecticut African-American regiment did serve during the American Civil War. The 29th Connecticut Volunteer Infantry (Colored) was organized in New Haven in March of 1864. They had trench duty outside of Petersburg and Richmond - hard, dangerous work - for almost a year. When Richmond was abandoned, they were first infantry regiment into the city. The 29th occupied some of the South's cities until November 1865.
The 29th's service has only been recently recognized. A group of descendants made sure than their ancestors were honored. Monuments to the regiment were erected in Danbury in 2007 and New Haven in 2008. The group's efforts have made information about the regiment widely available.