  We study the branching ratios and up-down asymmetries in the charmed baryon
weak decays of ${\bf B}_c\to {\bf B}_DM$ with ${\bf B}_{c(D)}$ anti-triplet
charmed (decuplet) baryon and $M$ pseudo-scalar meson states based on the
flavor symmetry of $SU(3)_F$. We propose equal and physical-mass schemes for
the hadronic states to deal with the large variations of the decuplet baryon
momenta in the decays in order to fit with the current experimental data. We
find that our fitting results of ${\cal B}({\bf B}_c\to {\bf B}_DM) $ are
consistent with the current experimental data in both schemes, while the
up-down asymmetries in all decays are found to be sizable, consistent with the
current experimental data, but different from zero predicted in the literature.
We also examine the processes of $\Xi_c^0 \to \Sigma^{\prime 0}K_S/K_L$ and
derive the asymmetry between the $K_L/K_S$ modes being a constant.
