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

Asymmetries in $B \to K^\ast \ell^+ \ell^-$ Decays and Two Higgs Doublet Model