  The nonleptonic weak decay of $\Lambda^+_c \to \bar{K}^0 \eta p$ is analyzed
from the viewpoint of probing the $N^*(1535)$ resonance, which has a big decay
branching ratio to $\eta N$. Up to an arbitrary normalization, the invariant
mass distribution of $\eta p$ is calculated with both the chiral unitary
approach and an effective Lagrangian model. Within the chiral unitary approach,
the $N^*(1535)$ resonance is dynamically generated from the final state
interaction of mesons and baryons in the strangeness zero sector. For the
effective Lagrangian model, we take a Breit-Wigner formula to describe the
distribution of the $N^*(1535)$ resonance. It is found that the behavior of the
$N^*(1535)$ resonance in the $\Lambda^+_c \to \bar{K}^0 N^*(1535) \to \bar{K}^0
\eta p$ decay within the two approaches is different. The proposed
$\Lambda^+_c$ decay mechanism can provide valuable information on the
properties of the $N^*(1535)$ and can in principle be tested by facilities such
as BEPC II and SuperKEKB.
