  We analyze the energy dependence for two types of parity-non-conserving
  (PNC) asymmetries in the reaction $\gamma D\to np$ in the near-threshold
region. The first one is the asymmetry in reaction with circularly polarized
photon beam and unpolarized deuteron target. The second one corresponds to
those with an unpolarized photon beam and polarized target. We find that the
two asymmetries have quite different energy dependence, and their shapes are
sensitive to the PNC-meson exchange coupling constants.
  The predictions for the future possible experiments to provide definite
constraints for the PNC-coupling constants are discussed.
