  Using the full data sample of 980 $\mathrm{fb}^{-1}$ collected with the Belle
detector at the KEKB asymmetric energy electron-positron collider, we report
the results of the first search for the rare semileptonic decays $\Xi_c^0 \to
\Xi^0\ell^+\ell^-$ ($\ell=e$ or $\mu)$. No significant signals are observed in
the $\Xi^0\ell^+\ell^-$ invariant-mass distributions. Taking the decay $\Xi_c^0
\to \Xi^- \pi^+$ as the normalization mode, we report 90\% credibility upper
limits on the branching fraction ratios ${\cal{B}} (\Xi_c^0 \to \Xi^0 e^+ e^-)
/ {\cal{B}}(\Xi_c^0\to \Xi^-\pi^+) < 6.7 \times 10^{-3}$ and ${\cal{B}}
(\Xi_c^0 \to \Xi^0 \mu^+ \mu^-) / {\cal{B}}(\Xi_c^0\to \Xi^-\pi^+) < 4.3 \times
10^{-3}$ based on the phase-space assumption for signal decays. The 90\%
credibility upper limits on the absolute branching fractions of ${\cal{B}}
(\Xi_c^0 \to \Xi^0 e^+ e^-)$ and ${\cal{B}} (\Xi_c^0 \to \Xi^0 \mu^+ \mu^-)$
are found to be $9.9 \times 10^{-5}$ and $6.5 \times 10^{-5}$, respectively.
