  We report searches for $B^0\to\rm{invisible}$ and
$B^0\to\rm{invisible}+\gamma$ decays, where the energy of the photon is
required to be larger than 0.5 GeV. These results are obtained from a
$711\,{\rm fb}^{-1}$ data sample that contains $772 \times 10^6 B\bar{B}$ pairs
and was collected near the $\Upsilon\,(4S)$ resonance with the Belle detector
at the KEKB $e^+ e^-$ collider. We observe no significant signal for either
decay and set upper limits on their branching fractions at $90\%$ confidence
level of $\mathcal{B}\,(B^0\to\rm{invisible}) < 7.8\times10^{-5}$ and
$\mathcal{B}\,(B^0\to\rm{invisible}+\gamma) < 1.6\times10^{-5}$.
