  Using data samples of $e^+e^-$ collisions collected at the $\Upsilon(1S)$,
$\Upsilon(2S)$, and $\Upsilon(3S)$ resonances with the Belle detector, we
search for the three-body decay of the $\Omega(2012)$ baryon to $K\pi\Xi$. This
decay is predicted to dominate for models describing the $\Omega(2012)$ as a
$K\Xi(1530)$ molecule. No significant $\Omega(2012)$ signals are observed in
the studied channels, and 90\% credibility level upper limits on the ratios of
the branching fractions relative to $K \Xi$ decay modes are obtained.
