  We make a study of the $\Omega_c(3120)$, one of the five $\Omega_c$ states
observed by the LHCb collaboration, which is well reproduced as a molecular
state from the $\Xi^*_c \bar K$ and $\Omega^*_c \eta$ channels mostly. The
state with $J^P = 3/2^-$ decays to $\Xi_c \bar K$ in $D$-wave and we include
this decay channel in our approach, as well as the effect of the $\Xi^*_c$
width. With all these ingredients, we determine the fraction of the
$\Omega_c(3120)$ width that goes into $\Xi_c \pi \bar K$, which could be a
measure of the $\Xi^*_c \bar K$ molecular component, but due to a relatively
big binding, compared to its analogous $\Omega(2012)$ state, we find only a
small fraction of about 3%, which makes this measurement difficult with present
statistics. As an alternative, we evaluate the scattering length and effective
range of the $\Xi^*_c \bar K$ and $\Omega^*_c \eta$ channels which together
with the binding and width of the $\Omega_c(3120)$ state, could give us an
answer to the issue of the compositeness of this state when these magnitudes
are determined experimentally, something feasible nowadays, for instance,
measuring correlation functions.
