Certain CP-odd momentum correlations in the production and subsequent decay of τ pairs in ${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{-}}$ collisions are enhanced significantly when the ${\mathit{e}}^{+}$ and ${\mathit{e}}^{\mathrm{-}}$ beams are longitudinally polarized. These may be used to probe the real and imaginary parts of ${\mathit{d}}_{\mathrm{\tau }}^{\gamma }$, the electric dipole moment of the τ. Closed-form expressions for these ‘‘vector correlations’’ and the standard deviation of the operators defining them due to standard model interactions are presented for the two-body final states of τ decays. If 42% average polarization of each beam is achieved, as proposed for the τ-charm factories, with equal integrated luminosities for each sign of polarization and a total yield of 2×${10}^7$ ${\mathrm{\tau }}^{+}$${\mathrm{\tau }}^{\mathrm{-}}$ pairs, it is possible to attain sensitivities for ‖δ Re${\mathit{d}}_{\mathrm{\tau }}^{\gamma }$‖ of 8×${10}^{\mathrm{-}19}$, 1×${10}^{\mathrm{-}19}$, 1×${10}^{\mathrm{-}19}$e cm, respectively, and for ‖δ Im${\mathit{d}}_{\mathrm{\tau }}^{\gamma }$‖ of 4×${10}^{\mathrm{-}14}$, 6×${10}^{\mathrm{-}15}$, 5×${10}^{\mathrm{-}16}$e cm, respectively, at the three operating center-of-mass energies of 3.67, 4.25, and 10.58 GeV. These bounds emerge when the effects of a possible weak dipole form factor ${\mathit{d}}_{\mathrm{\tau }}^{\mathit{Z}}$ are negligible as is the case when it is of the same order of magnitude as ${\mathit{d}}_{\mathrm{\tau }}^{\gamma }$. Furthermore, in such a polarization experiment where different polarizations are possible, a model-independent disentangling of their individual effects is possible, and a technique to achieve this is described. A strong longitudinal polarization physics program at the τ-charm factory appears warranted.

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