CP Violation in the Decay of Neutral Higgs Boson into $t-{\bar t}$ or $W^+-W^-$

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.