CP-violating asymmetries in both the production and the decays of s-channel neutral Higgs bosons at ,LL+,LL-colliders can be large. If the C P violation occurs in the muon-Higgs-boson coupling, one observes a production asymmetry with transversely polarized p+p-beams. Likewise if the C P violation occurs in the top-quark-Higgs-boson or r-Higgs-boson coupling, one observes an azimuthal decay asymmetry in @+,LL--t tf (or T+T-). C P studies at such colliders allow a uniquely clean way of deducing the underlying C P phases; in turn these parameters would significantly improve our understanding of baryogenesis.