  We report a measurement of the ratios of branching fractions $\mathcal{R}(D)
= {\cal B}(\bar{B} \to D \tau^- \bar{\nu}_{\tau})/{\cal B}(\bar{B} \to D \ell^-
\bar{\nu}_{\ell})$ and $\mathcal{R}(D^{\ast}) = {\cal B}(\bar{B} \to D^* \tau^-
\bar{\nu}_{\tau})/{\cal B}(\bar{B} \to D^* \ell^- \bar{\nu}_{\ell})$, where
$\ell$ denotes an electron or a muon. The results are based on a data sample
containing $772\times10^6$ $B\bar{B}$ events recorded at the $\Upsilon(4S)$
resonance with the Belle detector at the KEKB $e^+ e^-$ collider. The analysis
utilizes a method where the tag-side $B$ meson is reconstructed in a
semileptonic decay mode, and the signal-side $\tau$ is reconstructed in a
purely leptonic decay. The measured values are $\mathcal{R}(D)= 0.307 \pm 0.037
\pm 0.016$ and $\mathcal{R}(D^{\ast})= 0.283 \pm 0.018 \pm 0.014$, where the
first uncertainties are statistical and the second are systematic. These
results are in agreement with the Standard Model predictions within $0.2$ and
$1.1$ standard deviations, respectively, while their combination agrees with
the Standard Model predictions within $1.2$ standard deviations.
