  We have searched for the lepton-flavor-violating decay $B^{0}\to K^{\ast 0}
\mu^{\pm} e^{\mp}$ using a data sample of 711 $fb^{-1}$ that contains $772
\times 10^{6}$ $B\bar{B}$ pairs. The data were collected near the $\Upsilon
(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy
$e^{+}e^{-}$ collider. No signals were observed, and we set 90% confidence
level upper limits on the branching fractions of ${\cal B}(B^{0}\to K^{\ast 0}
\mu^{+} e^{-})< 1.2\times 10^{-7}$, ${\cal B}(B^{0}\to K^{\ast 0} \mu^{-}
e^{+})< 1.6\times 10^{-7}$, and, for both decays combined, ${\cal B}(B^{0}\to
K^{\ast 0} \mu^{\pm} e^{\mp}) < 1.8\times 10^{-7}$. These are the most
stringent limits on these decays to date.
