Higgs boson interference in mu^+ mu^- ->chargino_i chargino_j with longitudinally polarized beams

We study chargino production at a muon collider with longitudinally polarized beams and center of mass energies around the heavy neutral Higgs boson resonances. We show that the interference of the CP even and CP odd Higgs bosons can be analyzed using the energy distributions of the lepton or W boson from the chargino two-body decays \tilde\chi^\pm_j\to\ell^\mp\tilde\nu_\ell or \tilde\chi^\pm_j \to W^\pm \neutralino_1, respectively. The energy distributions depend on the longitudinal polarization of the decaying chargino, which are correlated to the muon beam polarizations. We define asymmetries in these energy distributions which allow a determination of the H and A couplings to the charginos and in particular of their relative phase. We analyze the asymmetries, cross sections and branching ratios in CP conserving Minimal Supersymmetric Standard Model scenarios. For nearly degenerate Higgs bosons we find maximal asymmetries which can be measured with high statistical significance.