  We study possible CP-violation effects of the Higgs to $Z$-boson coupling at
a future $e^+ e^-$ collider, e.g. the International Linear Collider (ILC). We
find that the azimuthal angular distribution of the muon pair, produced by $e^+
e^- \rightarrow H Z \rightarrow H \mu^+ \mu^-$, can be sensitive to such a
CP-violation effect when we apply initial transversely polarized beams. Based
on this angular distribution, we construct a CP sensitive asymmetry and obtain
this asymmetry by \texttt{Whizard} simulation. By comparing the SM prediction
with 2$\sigma$ range of this asymmetry, we estimate the discovery limit of the
CP-odd coupling in $HZZ$ interaction.
