  We discuss a general two-Higgs-doublet model with CP violation in the Higgs
sector. In general, the three neutral Higgs fields of the model all mix and the
resulting physical Higgs bosons have no definite CP properties. We derive a new
sum rule relating Yukawa and Higgs-Z couplings which implies that a neutral
Higgs boson cannot escape detection at an e^+e^- collider if it is
kinematically accessible in Z+Higgs, $b\anti b+$Higgs and $t\anti t+$Higgs
production, irrespective of the mixing angles and the masses of the other
neutral Higgs bosons. We also discuss modifications of the sum rules and their
phenomenological consequences in the case when the two-doublet Higgs sector is
extended by adding one or more singlets.
