  The $\mu^-e^-\to e^-e^-$ process in a muonic atom is one of the promising
probes to study the charged lepton flavor violation (CLFV). We have
investigated the angular distribution of electrons from the polarized muon of
the atomic bound state. The parity violating asymmetric distribution of
electrons is analyzed by using lepton wave functions under the Coulomb
interaction of a finite nuclear charge distribution. It is found that the
asymmetry parameters of electrons are very sensitive to the chiral structure of
the CLFV interaction and the contact/photonic interaction. Therefore, together
with the atomic number dependence of the decay rate studied in our previous
work, the angular distribution of electrons from a polarized muon should be a
very useful tool to constrain the model beyond the standard model.
