  We investigate CP-violation effects in the bosonic sector of the Standard
Model (SM) with two Higgs doublets. First we calculate the mass eigenstates of
the physical neutral Higgses for small but nonzero CP-violation parameter
$\xi_{\ast}$, and then a ``forward-backward'' asymmetry ${\cal A}_{fb}$ for the
decay $H \to W^+W^-Z$ that would be a signal of CP-violation. Although the
effects are in general small (${\cal A}_{fb} = \Gamma_{fb}/\Gamma \sim {\cal
O}(10^{-3})$), ${\cal A}_{fb}$ turns out to be a rather clean signal of
CP-violation, since neither the CP-conserving final state interactions nor the
direct production background events contribute to $\Gamma_{fb}$. The process is
a counterexample to the widespread belief that CP-violation processes must
involve fermions. The CKM-type CP-violation effects that could in principle
also contribute to ${\cal A}_{fb}$ are negligible. The nonzero ${\cal A}_{fb}$
could possibly be detected at some later stage in future colliders such as LHC
or SSC.
