  To improve the theoretical prediction of the anomalous dipole moments of the
$\tau$-neutrino, we have carried out a study through the process $\gamma e^-
\to \tau \bar\nu_\tau \nu_e$, which represents an excellent and useful option
in determination of these anomalous parameters. To study the potential of the
process $\gamma e^- \to \tau \bar\nu_\tau \nu_e$, we apply a future high-energy
and high-luminosity linear electron-positron collider, such as the CLIC, with
$\sqrt{s}=380, 1500, 3000\hspace{0.8mm}GeV$ and ${\cal L}=10, 50, 100, 200,
500, 1000, 1500, 2000, 3000\hspace{0.8mm}fb^{-1}$, and we consider systematic
uncertainties of $\delta_{sys}=0, 5, 10\%$. With these elements, we present a
comprehensive and detailed sensitivity study on the total cross-section of the
process $\gamma e^- \to \tau \bar\nu_\tau \nu_e$, as well as on the dipole
moments $\mu_{\nu_\tau}$ and $d_{\nu_\tau}$ at the $95\%$ C.L., showing the
feasibility of such process at the CLIC at the $\gamma e^-$ mode with
unpolarized and polarized electron beams.

High Energy Physics - Phenomenology