  We report on a theoretical study of the newly observed $\Omega(2012)$
resonance in the nonleptonic weak decays of $\Omega_c^0 \to \pi^+
\bar{K}\Xi^*(1530) (\eta \Omega) \to \pi^+ (\bar{K}\Xi)^-$ and $\pi^+
(\bar{K}\Xi\pi)^-$ via final-state interactions of the $\bar{K}\Xi^*(1530)$ and
$\eta \Omega$ pairs. The weak interaction part is assumed to be dominated by
the charm quark decay process: $c(ss) \to (s + u + \bar{d})(ss)$, while the
hadronization part takes place between the $sss$ cluster from the weak decay
and a quark-antiquark pair with the quantum numbers $J^{PC} = 0^{++}$ of the
vacuum, produces a pair of $\bar{K}\Xi^*(1530)$ and $\eta \Omega$. Accordingly,
the final $\bar{K}\Xi^*(1530)$ and $\eta \Omega$ states are in pure isospin $I=
0$ combinations, and the $\Omega_c^0 \to \pi^+ \bar{K}\Xi^*(1530)(\eta \Omega)
\to \pi^+ (\bar{K}\Xi)^-$ decay is an ideal process to study the $\Omega(2012)$
resonance. With the final-state interaction described in the chiral unitary
approach, up to an arbitrary normalization, the invariant mass distributions of
the final state are calculated, assuming that the $\Omega(2012)$ resonance with
spin-parity $J^P = 3/2^-$ is a dynamically generated state from the coupled
channels interactions of the $\bar{K}\Xi^*(1530)$ and $\eta \Omega$ in $s$-wave
and $\bar{K}\Xi$ in $d$-wave. We also calculate the ratio,
$R^{\bar{K}\Xi\pi}_{\bar{K}\Xi} = {\rm Br}[\Omega_c^0 \to \pi^+ \Omega(2012)^-
\to \pi^+ (\bar{K}\Xi \pi)^-] / {\rm Br}[\Omega_c^0 \to \pi^+ \Omega(2012)^-
\to \pi^+ (\bar{K}\Xi)^-$]. The proposed mechanism can provide valuable
information on the nature of the $\Omega(2012)$ and can in principle be tested
by future experiments.
