Using a sample of 4,500 polarized Z decays to[tau] lepton pairs accumulated with the SLD detector at the SLAC Linear Collider (SLC) in 1993-95, a search has been made for anomalous couplings in the neutral current reaction e[sup+]e[sup[minus]][yields][tau][sup+][tau][sup[minus]]. A measurement of the CP violating Weak Electric Dipole Moment (WEDM) and the CP conserving Weak Magnetic Dipole Moment (WMDM) of the[tau] lepton has been performed by considering the transverse spin polarization of[tau] leptons produced at the Z pole. Using a maximum likelihood technique, the observed[tau] decay spectra in the e, [mu], [pi], and[rho] decay channels are used to infer the net transverse polarization of the underlying tau leptons, and a fit for the anomalous dipole moments is performed. No evidence for these dipole movements is observed, and limits are placed on both the real and imaginary parts of the WEDM and WMDM.