  The recently discovered scalar resonance at the LHC is now almost confirmed
to be a Higgs Boson, whose CP properties are yet to be established. At the ILC
with and without polarized beams, it may be possible to probe these properties
at high precision. In this work, we study the possibility of probing departures
from the pure CP-even case, by using the decay distributions in the process
$e^+ e^- \to t \bar{t} \Phi$, with $\Phi$ mainly decaying into a $b\bar b$
pair. We have compared the case of a minimal extension of the SM case (Model I)
with an additional pseudoscalar degree of freedom, with a more realistic case
namely the CP-violating Two-Higgs Doublet Model (Model II) that permits a more
general description of the couplings. We have considered the ILC with
$\sqrt{s}=800$\,GeV and integrated luminosity of $300\, {\rm fb}^{-1}$. Our
main findings are that even in the case of small departures from the CP-even
case, the decay distributions are sensitive to the presence of a CP-odd
component in Model II, while it is difficult to probe these departures in Model
I unless the pseudoscalar component is very large. Noting that the proposed
degrees of beam polarization increases the statistics, the process demonstrates
the effective role of beam polarization in studies beyond the Standard Model.
Further, our study shows that an indefinite CP Higgs would be a sensitive
laboratory to physics beyond the SM.
