CP violation in the $\mu \to 3e$ process and supersymmetric grand unified theory

A triple vector correlation in the ${\mu }^{+}\to e^{+}{e}^{+}{e}^{-}$ decay with polarized muons is investigated as a probe to CP violating coupling constants in supersymmetric models. A sizable triple correlation can be induced due to a complex phase in the supersymmetric soft-breaking terms in the SU(5) grand unified theory. Correlation with the electric dipole moments of electron and neutron are investigated and it is shown that these quantities give independent information on possible CP violating sources.