  It has recently been shown that by measuring the transverse polarization of
the final particles in the LFV processes $\mu \to e\gamma$, $\mu \to eee$ and
$\mu N\to e N$, one can derive information on the CP-violating phases of the
underlying theory. We derive formulas for the transverse polarization of the
final particles in terms of the couplings of the effective potential leading to
these processes. We then study the dependence of the polarizations of $e$ and
$\gamma$ in the $\mu \to e \gamma$ and $\mu N \to e N$ on the parameters of the
Minimal Supersymmetric Standard Model (MSSM). We show that combining the
information on various observables in the $\mu \to e\gamma$ and $\mu N\to e N$
search experiments with the information on the electric dipole moment of the
electron can help us to solve the degeneracies in parameter space and to
determine the values of certain phases.
