The group Reclaim the Records has gotten an index for Connecticut vital records that covers more than the above indexes and also has a birth index.
https://www.connecticutgenealogy.org/This "includes the first-ever online publication of Connecticut birth index data from 1897-1917, and this new data is the only statewide index of Connecticut births that exists publicly online anywhere. (Yay!) We also acquired marriage and death index data from 1897 through 2017, while the next most complete online version of the index only had data through 2012. And our search engine is set up to better handle some of the weirdness in this data, such as the official records from 1969-1979 only having the first five letters of each person’s given name, and some of the pre-1925 data missing some names entirely. Our search engine also has all the fun bells and whistles like automatic nickname and partial name searches, wildcard searches, automatic typo or letter transposition searches, date range searches (even down to the exact day, not just the year), and so on.
And we even geo-coded all the data, and we also auto-supplemented all the data with county names.
That means you can use this new website to do much more complicated things with this data, like search for every person named Elizabeth and no last name provided, and in any type of Connecticut record dated between July 13, 1902 and February 8, 1903, and within 25 miles of the town of Hamden — and get back hundreds of results that might help you find her, even if she was listed in the record as Eliza, Lizzie, Bessie, or Elise. You can even make queries like “show me all births in Town X or County Y in early August 1908” without specifying any name data at all which is so important when it comes to finding that elusive relative’s record, especially because we’ve discovered that over 100,000 of these records (particularly ones from pre-1925) are missing a given name, a surname, or both, often due to the original handwritten records’ illegibility."
https://www.reclaimtherecords.org/records-request/30/
