  It is shown that the rare decays $Z \to \nu \bar{nu} \gamma$ and $Z \to \nu
\bar{\nu} \gamma \gamma$ are useful to put model-independent bounds on
neutrino-one-photon and neutrino-two-photon interactions. The results are then
used to constrain the $\tau$ neutrino magnetic moment and the double radiative
decay $\nu_j \to \nu_i \gamma \gamma$. It is found that the decay $Z \to \nu
\bar{nu} \gamma$ gives a more stringent bound on the $\tau$ neutrino magnetic
moment than that obtained from $Z \to \nu \bar{\nu} \gamma \gamma$; the latter
decay in turn gives limits on the neutrino-two-photon interaction that are less
stringent than those obtained for a sterile neutrino $\nu_s$ from the analysis
of $\nu_\mu N \to \nu_s N$ conversion.
