  We perform a systematic study of the production of a third-generation
fermion-pair, $\mu^+\mu^-\to f\bar{f}$ for $f=\tau^-,b$, and t in the minimal
supersymmetric standard model (MSSM) with explicit CP violation, which is
induced radiatively by soft trilinear interactions related to squarks of the
third generation. We classify all the observables for probing the CP property
of the Higgs bosons constructed by the initial muon beam polarization along
with the unpolarized final fermions and with the final-fermion polarization
configuration of equal helicity, respectively. The observables allow for
complete determination of CP property of the neutral Higgs bosons. The
interference between the Higgs boson and gauge boson contributions also could
provide a powerful method for the determination of the CP property of two heavy
Higgs bosons in the top-quark pair production near the energy region of the
Higgs-boson resonances. For the lightest Higgs-boson mass there is no sizable
interference between scalar and vector contributions for the determination of
the CP property of the lightest Higgs boson. We give a detailed numerical
analysis to show how the radiatively-induced CP violation in the Higgs sector
of the MSSM can be measured.
