  We study the general Higgs-weak boson coupling with CP-violation via the
process e+e- -> f \bar f h. We categorize the signal channels by sub-processes
Zh production and ZZ fusion and construct four CP asymmetries by exploiting
polarized e+e- beams. We find complementarity among the sub-processes and the
asymmetries to probe the real and imaginary parts of the CP-violating form
factor. Certain asymmetries with unpolarized beams can retain significant
sensitivity to the coupling. We conclude that at a linear collider with high
luminosity, the CP-odd ZZh coupling may be sensitively probed via measurements
of the asymmetries.
