B-> X_d ell^+ell^- in a CP softly broken two Higgs doublet model

We study the differential branching ratio, forward-backward asymmetry, CP-violating asymmetry, CP-violating asymmetry in the forward-backward asymmetry and polarization asymmetries of the final lepton in the B-> X_d \ell^+\ell^- decays in the context of a CP softly broken two Higgs doublet model. We analyze the dependencies of these observables on the model parameters by paying a special attention to the effects of neutral Higgs boson (NHB) exchanges and possible CP violating effects. We find that NHB effects are quite significant for the \tau mode. The above-mentioned observables seems to be promising as a testing ground for new physics beyond the SM, especially for the existence of the CP-violating phase in the theory.