  We study the influence of a charged-Higgs on the excess of branching fraction
ratio, $R_M = BR(\bar B \to M \tau \bar\nu_\tau)/BR(\bar B \to M \ell \bar
\nu_\ell)$ $(M=D, D^*)$, in a generic two-Higgs-doublet model. In order to
investigate the lepton polarization, the detailed decay amplitudes with lepton
helicity are given. When the charged-Higgs is used to resolve excesses, it is
found that two independent Yukawa couplings are needed to explain the $R_D$ and
$R_{D^*}$ anomalies. We show that when the upper limit of $BR(B_c \to \tau \bar
\nu_\tau)<30\%$ is included, $R_D$ can be significantly enhanced while
$R_{D^*}<0.27$. With the $BR(B_c\to \tau \bar \nu_\tau)$ constraint, we find
that the $\tau$-lepton polarizations can be still affected by the charged-Higgs
effects, where the standard model (SM) predictions are obtained as: $P^\tau_{D}
\approx 0.324$ and $P^\tau_{D^*}\approx -0.500$, and they can be enhanced to be
$P^\tau_{D} \approx 0.5$ and $P^\tau_{D^*} \approx -0.41$ by the charged-Higgs.
The integrated lepton froward-backward asymmetry (FBA) is also studied, where
the SM result is $\bar A^{D^{(*)},\tau}_{FB} \approx -0.359(0.064)$, and they
can be enhanced (decreased) to be $\bar A^{D^{(*)},\tau}_{FB} \approx -0.33
(0.02)$.
