  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.
