On behalf of the J-PET CollaborationA first result related to a CPT test in the decay of ortho-positronium based on data collected by means of the J-PET detector is already available, 1 and a new test of CP symmetry is under investigation. 2 Both results are based on the determination of angular correlations between momenta of gamma rays and other vector properties of the investigated system. 3 Here, arguments for the possible usage of data collected by the J-PET group to test CPT symmetry within the Standard-Model Extension framework 4 are shortly presented.