The Dubious Paper is a piece of paper with an image of a star on it.
Once Mario acquires the Super Hammer, he can head into one of the minor league rooms and destroy a large yellow block. Behind where the block once was is a secret room and the Dubious Paper can be seen on an upper ledge where Mario must use Yoshi to get to it. Upon reading it, Mario and Yoshi are shocked to learn that the Dubious Paper is about the Crystal Star. Before they read any more, Jolene enters into the room and takes the Dubious Paper.
The Dubious Paper most likely belongs to Grubba as he has a device under the Glitz Pit arena that uses the power of the Crystal Star to drain the life force from fighters into him. The Dubious Paper may be plans for that device.