  The study of polarized branching ratio and different lepton polarization
asymmeteries in the exclusive rare decays $B\rightarrow
K^{\ast}\ell^{+}\ell^{-}$ ($\ell=\mu , \tau$) have been made in the standard
model (SM) and in type III of the THDM. It has been found that the effects
arise from the THDM are quite promising in the longitudinal and transverse
polarized branching ratios $(\mathcal{B}_{L, T})$. Likewise, in case of $\mu$'s
as final state leptons, the polarized branching ratios have an order of
magnitude difference from their SM results. Similar trends have also been
observed both in the longitudinal and normal lepton polarization asymmetries
$P_{L, N}$ as well as their average values. We hope that the possible
signatures of these observables in $B\rightarrow K^{\ast}\ell^{+}\ell^{-}$
decays at different on going and future experiments will serve as a good tool
in the indirect searches of an extra Higgs boson doublet.
