  Polarization characteristics of gamma gamma and gamma Z states in the Higgs
boson decays h -> gamma gamma and h -> gamma Z are discussed. Based on
effective Lagrangian, describing h gamma gamma and h gamma Z interactions with
CP-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 parameter
xi_2, arises due to presence of both parts in effective Lagrangian and its
non-Hermiticity. The circular polarization is proportional to the
forward-backward asymmetry of fermions in the decay h -> gamma Z -> gamma f
bar{f}. Measurement of this observable would allow one to search for deviation
from the standard model and possible violation of CPT symmetry. We discuss also
a possibility to measure parameters xi_1, xi_3, describing correlation of
linear 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 zero
will indicate CP violation in the Higgs sector.
