  We report the results of the first search for Standard Model and
baryon-number-violating two-body decays of the neutral $B$ mesons to
$\Lambda^{0}$ and $\Omega^{(*)0}_c$ using 711~${\rm fb^{-1}}$ of data collected
at the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB
asymmetric-energy $e^+ e^-$ collider. We observe no evidence of signal from any
such decays and set 95\% confidence-level upper limits on the products of $B^0$
and $\bar{B}^0$ branching fractions for these two-body decays with
$\mathcal{B}(\Omega_{c}^{0} \to \pi^+ \Omega^-)$ in the range between
9.5~$\times 10^{-8}$ and 31.2~$\times 10^{-8}$.
