  We study possible anomalous CP-violating Higgs couplings to mu mu-bar and t
t-bar fully model-independent way through top-quark pair productions at muon
colliders. Assuming additional non-standard neutral Higgs bosons, whose
couplings with top-quark and muon are expressed in the most general covariant
form, we carry out analyses of effects which they are expected to produce via
CP-violating asymmetries and also the optimal-observable (OO) procedure under
longitudinal and transverse muon polarizations. We find the measurement of the
asymmetry for longitudinal beam polarization could be useful to catch some
signal of CP violation, and an OO analysis might also be useful if we could
reduce the number of unknown parameters with a help of other experiments and if
the size of the parameters is at least O(1) ~ O(10).
