Probate Record Volumes are the official record of the Probate Court. The Volumes are typically arranged chronologically with Indexes at the beginning. A vast amount of Record Volumes were microfilmed many years ago. This microfilm has been digitized and is available through a Place search of the FamilySearch catalog. For example, this link will bring you to the catalog record for Hartford Probate Record Volumes from 1649-1932. The camera symbol under the format column will bring you to the digitized volumes!
To find out what Probate District had administration over the town where an ancestor lived, consult the Probate Court Finding Aids. The finding aids identify the proper probate court for a given Connecticut city or town and indicates what probate materials (and whether original or on microfilm) are available. It shows the probate district(s) to which each Connecticut town has been assigned; the locations of original estate papers and record books, and whether the items have been microfilmed.
Andover Probate Court Record Volume 10, Cynthia Alvord's Will