  We study the differential branching ratio, forward-backward asymmetry,
CP-violating asymmetry, CP-violating asymmetry in the forward-backward
asymmetry and polarization asymmetries in the $B -> K \ell^+ \ell^-$ and $B ->
K^* \ell^+ \ell^-$ 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 both decays. A combined analysis of above-mentioned
observables seems to be very promising as a testing ground for new physics
beyond the SM, especially for the existence of the CP-violating phase in the
theory.
