Every state has some unique genealogy resources available. My family history in Connecticut dates back about 400 years and I am proud to say I am a descendat of one of the founders of Hartford. Now since my family does go back several hundred years in Connecticut I have spent a lot of time at the CT State Library and learned firsthand about several of the unique resources available for researching the state. I had the advantage of using them on site and learning from the library staff but the great news is they are also available on microfilm at any LDS Family History Center.
The Barbour Collection
Lucius Barnes Barbour was the State Examiner of Public Records from 1911-1934. He had directed the publication of the Bolton and Vernon vital records by the Connecticut Historical Society in 1909. While he was the state examiner he expanded this project to publish the existing vital records for almost all Connecticut towns up through about 1850. A volume of vital records was published for each town in Connecticut as part of the project and a statewide index was created.
The original paper index for this collection is still available for use at the state library. The books for each town are also still available for purchase if you hunt around amazon a bit but they average about $30 each. Unless your family was in the same town for several generations I recommend just using the microfilm.
The index can be used at the Connecticut State Library or the microfilm can be ordered through an LDS Family History Center. The advantage of going to the library is you have the entire index available in one place rather than having to order multiple parts of the index on microfilm. Once you find an item in the index your next step would be to get a copy of the vital record. Because these records have so little information in them, what you find in the index is usually the same information that exists in the actual town record. I usually do not bother with official birth, marriage or death certificates prior to 1850.
In 1917, the state of Connecticut conducted a state census in preparation for WWI to identify the skills of men of age for military service. This can be an interesting picture of your ancestor as it asked a number of questions to identify current citizenship, occupation and skills such as driving a team (of horses) or driving an automobile. It also asked the respondents to list any previous military experience. This can also help bridge the gap between the 1910 and 1920 census.
This census has an alphabetical index to for you to lookup the name of the person you are interested in which will direct you to the full form. The index is arranged by town and then alphabetically within each town so you have to have some idea of where your ancestor lived. Only males over the age of 16 at the time of the census are included.
This census can be accessed at the Connecticut State Library or the microfilm can be ordered through an LDS Family History Center. You will have to look up your ancestor in the index then use the serial number listed to get the actual document with your ancestors information.
The Hale Collection
Just as the original Federal Census records were created using WPA funds, Connecticut used their WPA funds to index all the headstones in the state at that time. The index is named for Charles R. Hale who was the director of the project. Luckily for anyone with an interest in headstones he was determined to create a complete index and uncovered many abandoned and forgotten cemeteries as part of the indexing process. For example, the town clerk in North Stonington knew of only nine cemeteries in the town, Mr. Hale found 95.
The indexing process lasted from 1932-1935 so it is only helpful for burials prior to that time. Mr. Hale was very thorough and the index also includes small family cemeteries so this is worth checking out even if family legend says great-grandma was buried on the family farm. Speaking as someone whose family farm is now a golf course, this may be the only way to find an old family cemetery.
The index can be used at the Connecticut State Library or the microfilm can be ordered through an LDS Family History Center.