  Evidence for CP violation in baryonic decays has not been seen in
experiments. With large data events accumulated at $e^+e^-$ collider or Large
Hadron Collider, the charmed baryon decays would provide a promising laboratory
to test the CP symmetry. In this work, we formulate the $\Lambda_c^+\to\phi p$
and $ \Lambda_c^+\to\omega p$ decays for the measurements of their asymmetry
parameters in weak decays at the BESIII or the LHCb experiments. The
polarization transfer is analyzed in the two processes of $e^+ e^-
\to\Lambda_c^+\bar\Lambda_c^-$ and $\Lambda_b^0\to \Lambda^+_c\pi^-$, and the
formulas of the joint angular distribution for these processes are provided.
The sensitivity of the measurement of asymmetry parameters for the above two
decay processes is estimated for the future experiments.
