Prior to 84, the only GM factory installed Corvette hatchback was in the 82 Collector Editions. During the 70's, a fastback window conversion was available for converting 68-77 coupes. It was basically a flat piece of glass that was installed between the roof "sail panels", after the tunneled rear window and rear deck between the sail panels was removed. These were made made by Ecklers, I think, and may have been available in an openning version.
The 82 Collectors Edition hatch was made by Cars & Concepts. Cars & Concepts did t-top , sunroof and I think full convertible conversions on many different cars. They did conversions directly for the automakers, and also had locations around the country that did dealer and private customer conversions. The Corvette hatch conversion was released in 1979. I have seen quite a few of these conversions on 79-82 Corvettes. This may be because Cars & Concepts had a plant near me in Cinnaminson, NJ. These hatches were also installed in the Corvettes raffled by the NCCC to benefit Spina Bifida in 79-81. Chevrolet concidered installing the hatches in 81 Corvettes when production began at the new Bowling Green plant in June 81, but in the end, only offered them as factory installed in 82 Collector cars. The hatches used in the 82 CE cars came from Cars & Concepts, but were installed by Chevrolet.
A number of 74-77 Corvettes have had 78-82 big window rear clips installed on them. It's possible that you have a 77 that has had a 78-82 rear clip installed, along with the rear window hatch conversion. As posted by Easy Mike, a couple of photos would go a long way toward identifing what you have.