Grandmother Adopted in CT from NYC Agency

I've lurked here quiet a bit and finally joined the other day. I'm looking for some direction regarding our special situation (or perhaps not-so-special). My grandmother was adopted in the late 1910's in the CT court system from a NYC agency. In the 1960's, she was able to get a copy of her birth certificate by order of the Probate Court here in CT. We know her birth name and that of her mother. We've contacted the agency and were given an abstract of the info (as well as picture of her when she was a beautiful teenage girl...sent to the agency by my gm's adopted family to show she was progressing into a fine young lady). The abstract told us that my gm's birth mother was ALSO put up for adoption (but at a much later age). The mother eventually left the orphanage without being adopted. I do also know that the intake paperwork for my grandmother has all the historical information on her birthmother as well as the identity of her father and the birthmother's parents. Is there a way, through the CT court system, to access these records as the adoption went through the system here. The CT Probate Court has lost the original records but we do have the order for adoption from the records books. Can someone give me some guidance on if we can do something to access the private agency's records? They still exist and still have the records. Thank you for your time, PTG