  We investigate a potentially large CP violating asymmetry in the neutral
Higgs boson decay into a heavy quark pair or a $W^+$--$W^-$ pair. The source of
the CP nonconservation is in the Yukawa couplings of the Higgs boson which can
contain both scalar and pseudoscalar pieces. One of the interesting consequence
is the different rates of the Higgs boson decays into CP conjugate polarized
states. The required final state interactions can be either the strong or the
electroweak interactions. The CP violating asymmetry can manifests itself in
the asymmetry in the energies of the secondary decay products of these heavy
quarks and $W$ bosons. Such asymmetry can be measureable in the future
colliders such as SSC or LHC.
