  Bounds on the anomalous magnetic moment and the electric dipole moment of the
$\tau$-neutrino are calculated through the reaction $e^{+}e^{-}\to \nu \bar \nu
\gamma$ at the $Z_1$-pole, and in the framework of a left-right symmetric
model. The results are based on the recent data reported by the L3
Collaboration at CERN LEP. We find that the bounds are almost independent of
the mixing angle $\phi$ of the model in the allowed experimental range for this
parameter. In addition, the analytical and numerical results for the
cross-section have never been reported in the literature before.
