  It has recently been shown that by measuring the transverse polarizations of
the final particles in $\mu^- \to e^- e^+ e^-$, it is possible to extract
information on the phases of the effective couplings leading to this decay. We
examine this possibility within the context of R-parity violating Minimal
Supersymmetric Standard Model (MSSM) in which the $\mu^- \to e^- e^+e^-$
process can take place at a tree level. We demonstrate how a combined analysis
of the angular distribution of the emitted positrons and their transverse
polarization can determine the CP-violating phases of the trilinear R-parity
violating Yukawa couplings.
