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 \rightarrow 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.

PACS numbers: 12.60.Fr, 13.20.He