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Polarization characteristics of gamma gamma and gamma Z states in the Higgsboson decays h -> gamma gamma and h -> gamma Z are discussed. Based oneffective Lagrangian, describing h gamma gamma and h gamma Z interactions withCP-even and CP-odd parts, we calculate polarization parameters xi_1, xi_2,xi_3. A nonzero value of the photon circular polarization, defined by parameterxi_2, arises due to presence of both parts in effective Lagrangian and itsnon-Hermiticity. The circular polarization is proportional to theforward-backward asymmetry of fermions in the decay h -> gamma Z -> gamma fbar{f}. Measurement of this observable would allow one to search for deviationfrom the standard model and possible violation of CPT symmetry. We discuss alsoa possibility to measure parameters xi_1, xi_3, describing correlation oflinear polarizations of photon and Z boson, in the decay h -> gamma* Z -> l+ l-Z via distribution over the azimuthal angle between the decay planes of gamma*-> l+ l- and Z -> f bar{f}. Deviation of the measured value of xi_1 from zerowill indicate CP violation in the Higgs sector.

Polarization effects in the Higgs boson decay to gamma Z and test of CP and CPT symmetries