From the Super Mario Wiki
Mario's Star is an item of Mario that Luigi finds in Luigi's Mansion. It is found in the Observatory of the mansion, accessible after shooting the moon with a Meteor Ghost, a layer of ground will appear, on the other side, there is the star. This possession, along with Mario's Glove, Mario's Cap, Mario's Letter and Mario's Shoe are scattered around the mansion. If Luigi takes them to Madame Clairvoya, she will use her crystal ball to "communicate" with Mario.