  A 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, and a
new test of CP symmetry is under investigation. Both results are based on the
determination of angular correlations between momenta of gamma rays and other
vector properties of the investigated system. Here, arguments for the possible
usage of data collected by the J-PET group to test CPT symmetry within the
Standard-Model Extension framework are shortly presented.
