  We report the first measurement of the $\tau$ lepton polarization in the
decay ${\bar B} \rightarrow D^* \tau^- {\bar\nu_{\tau}}$ as well as a new
measurement of the ratio of the branching fractions $R(D^{*}) =
\mathcal{B}({\bar B} \rightarrow D^* \tau^- {\bar\nu_{\tau}}) /
\mathcal{B}({\bar B} \rightarrow D^* \ell^- {\bar\nu_{\ell}})$, where $\ell^-$
denotes an electron or a muon, with the decays $\tau^- \rightarrow \pi^-
\nu_{\tau}$ and $\tau^- \rightarrow \rho^- \nu_{\tau}$. We use the full data
sample of $772 \times 10^6$ $B{\bar B}$ pairs accumulated with the Belle
detector at the KEKB electron-positron collider. Our preliminary results,
$R(D^*) = 0.276 \pm 0.034{\rm (stat.)} ^{+0.029} _{-0.026}{\rm (syst.)}$ and
$P_{\tau} = -0.44 \pm 0.47 {\rm (stat.)} ^{+0.20} _{-0.17} {\rm (syst.)}$, are
consistent with the theoretical predictions of the Standard Model within $0.6$
standard deviation.
