  Lepton flavor violating processes $\mu \to e \gamma$ and $\mu \to 3e$ with
polarized muons are studied in the supersymmetric grand unified theory (SUSY
GUT). As a result of a detailed numerical calculation, it is shown that the P-
and T-odd asymmetries defined with the help of the muon polarization and the
ratio of two branching fractions make a good contrast between the SU(5) and
SO(10) SUSY GUT. These observables are useful to extract differences of the two
theories. In particular, the P-odd asymmetry of $\mu \to e \gamma$ varies
100%--100% in SO(10) whereas it is 100% in SU(5) and the T-odd asymmetry of
$\mu \to 3e$ can reach 15% in SU(5) within the EDM constraints whereas it is
small in SO(10).
