Did your ancestor serve in the Connecticut General Assembly? Why should you care? If your ancestor served in the General Assembly, he may have appeared in one of the many biographical sketch books of the legislature. And even if he doesn't - you may be able to learn more about his personality by seeing which political party he supported.
Stumped on how to get started? Try the Members of the Connecticut General Assembly database from the Connecticut State Library. The database has entries for all members from 1849 to 2008 and goes back much further if your ancestor served in the Senate. You can search by chamber, town, name, and party. I tried one ancestor's last name and received a nice surprise. In addition to the man I knew about, at least three other ancestors had served.