We investigate the prospects of the search for a nonzero $tau$ EDM form factor $d_tau(s)$ in $tau$ pair production by $e^+ e^-$ collisions at BEPC-II collider energies. We compute the expectation values and covariances of simple and optimal $CP$-odd observables for $tau$-pair production at $sqrt{s}=4.18$ GeV and $4.95$ GeV with subsequent decays of $tau^pm$ into major leptonic or semihadronic modes. For the $tau$ decays to two pions and three charged pions we take the full kinematic information of the hadronic system into account. Applying cuts and using realistic assumptions on the eventually attainable integrated luminosities at these energies, ${cal L}(4.18) = 3times 10^4~{rm pb}^{-1}$ and ${cal L}(4.95) = 10^4~{rm pb}^{-1}$, respectively, we find the following. By taking into account purely semihadronic and semihadronic-leptonic $tau^+tau^-$ decays one can achieve with optimal $CP$-odd observables the 1 s.d. sensitivities $delta {rm Re} d_tau = 4.5times 10^{-18}$ ecm ($5.3times 10^{-18}$ ecm) and $delta {rm Im} d_tau = 2.2 times 10^{-18}$ ecm ($2.7times 10^{-18}$ ecm) at $sqrt{s}=4.18$ GeV ($4.95$ GeV).
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