CP-violating dipole moments of leptons vanish at least to three loop order and are estimated to be (m(l)/MeV) X 1.6 X 10(-40) e cm in the standard model (SM), where m(l) is the mass of the lepton. However, they can receive potentially large contributions in some beyond the SM scenarios and this makes them very sensitive probes of new physics. In this article we show that a nonuniversal interaction, involving leptoquarks to the quark-lepton pair of the third generation through helicity-unsuppressed couplings of the order of ordinary gauge couplings, can generate electric and weak dipole moments of the order of 10(-19) e cm for the tau lepton. This is greater than purl supersymmetric (SUSY) and left-right (LR) contributions by almost three orders of magnitude. It is also greater than the mirror fermionic contribution by an order of magnitude. The measurements of d(tau)(z) and d(tau)(gamma) CERN LEP, SLC, and TCF are expected to reach sensitivities of 10(-18) e cm and 10(-19) e cm, respectively, in the near future. The observation of a nonvanishing dipole moment of tau at these facilities would, therefore, strongly favor superstring-inspired light leptoquark-mediated interactions, over pure SUSY or LR interactions and perhaps also mirror-generated mixings without some sort of quark-lepton unification as its origin.