Every genealogists has a great story of how finding a gravestone "solved" a brick wall. So how do you find that gravestone in Connecticut?
1. If your ancestor died after 1930, your best bet is probably the website Find A Grave. However, there are other options. Some towns have public cemeteries. A web search should help provide some hints.
2. For a burial prior to 1930, you have the option of the Hale Collection. Long story short, it is a long list of gravestone inscriptions. It's available several different ways, including microfilm and website.
If you're looking for an older stone and know the town, try the Hale Collection. Such stones are sometimes missing from Find A Grave. However, if you don't know the town, start with Find A Grave. The Hale Collection lacks a central index. Good luck!