We study normal (to the collision plane) and transverse (within the co
llision plane) single-tau polarization in tau pairs produced in e+ e-
unpolarized collisions at the Z-resonance. The transverse polarization
component is sensitive to the anomalous weak-magnetic moment, whereas
the normal polarization component is sensitive to a CP-violating weak
-electric dipole moment. We show how these components of the single ta
u polarization are accessible from the angular distribution of its dec
ay products. We define a CP violating asymmetry of the tau decay produ
cts which, with 10(7) Z's produced, provides a sensitivity of 2.3 x 10
(-18) e . cm for the weak-electric dipole moment.