Sleeping Giant has been closed since May 2018. A tornado came through and knocked down many trees near the main entrance to and major parking lot for the park (on Mount Carmel Avenue across from Quinnipiac University).
This entrance area has been cleared and is being rebuilt. The picnic and pavilion areas were also affected (though less so) and will be renovated also.
In the past the picnic shelter and pavilion areas were well shaded by trees and were a wonderful place to bring the family or even large groups of people for a party. This will presumably be so at some point in the future after the park re-opens.
There were Sleeping Giant Park campground sites which could be reserved and used for tent camping back in the twentieth century. I remember them from the 1980s. They have not been available for many years now.