  The benchmark mode $\Omega_c^0\to \Omega^- \pi^+$, which receives purely
factorization contribution, is of great importance among all the decay channels
of $\Omega_c^0$ decays. In this work, within the framework of non-relativistic
quark model (NRQM), we calculate all the 6 baryon transition form factors
involving $\frac12 ^+\to \frac32 ^+$ decays. The absolute branching fractions
of non-leptonic decays $\Omega_c^0\to \Omega^- \pi^+$, $\Omega_c^0\to \Omega^-
\rho^+$ and $\Omega_c^0\to \Xi^- \pi^+$ as well as semi-leptonic decays
$\Omega_c^0\to \Omega^- \ell^+ \nu_{\ell} \; (\ell=e,\mu)$ are calculated
although they cannot be measured directly by current experiment. Based on the
prediction $\mathcal{B}(\Omega_c^0\to\Omega^-\pi^+)=3.43\%$ in our work, we
further predict the ratios between interested modes and the benchmark mode,
giving $R(\Xi^-\pi^+)=0.156$, $R(\Omega^-\rho^+)=5.33$, $R(\Omega^-
e^+\nu_e)=1.18$ and $R(\Omega^- \mu^+\nu_\mu)=1.11$. The predictions on
$\Omega_c^0\to \Xi^-\pi^+$ and $\Omega_c^0\to \Omega^- e^+\nu$ agree well with
recent measured ratios reported by LHCb in 2023 and ALICE in 2024,
respectively.
