  Radiatively decaying dark matter may be searched through investigating the
photon spectrum of galaxies and galaxy clusters. We explore whether the
properties of dark matter can be constrained through the study of a
polarization state of emitted photons. Starting from the basic principles of
quantum mechanics we show that the models of symmetric dark matter are
indiscernible by the photon polarization. However, we find that the asymmetric
dark matter consisted of Dirac fermions is a source of circularly polarized
photons, calling for the experimental determination of the photon state.
