  We search for the process $B^0 \to \pi^- \tau^+ \nu_\tau$ using the full
Belle data set of $711\,{\rm fb}^{-1}$, corresponding to $772 \times 10^6
B\bar{B}$ pairs, collected at the $\Upsilon(4S)$ resonance with the Belle
detector at the KEKB asymmetric-energy $e^+ e^-$ collider. We reconstruct one
$B$ meson in a hadronic decay and search for the $B^0 \to \pi^- \tau^+
\nu_\tau$ process in the remainder of the event. No significant signal is
observed and an upper limit of $\mathcal{B}(B^0 \to \pi^- \tau^+ \nu_\tau) <
2.5 \times 10^{-4}$ is obtained at the $90\%$ confidence level.
