The headliner panel in my 09 DTS has come loose above the rear window and is hanging down about an inch. I have not been able to re-attach it by pressing it back up so it must be held in place some other way (unless I didn't use enough force).

How is the rear of the panel attached to the inner roof?

 

Most modern headliners are foam backed fabric spray glued to a poly board. Poly board is held to roof with trim moldings and Velcro.