  In this note, we analyze various constraints on the ``visible'' decay modes
of a massive $\tau $ neutrino, $\nu_\tau\rightarrow\nu^\prime\,\gamma $ and
$\nu_\tau\rightarrow\nu^\prime\, e^+ e^-$, where $\nu^\prime$ is a light
neutrino. The BEBC beam dump experiment provides model-independent constraints
on these modes. The lifetime for the $\nu^\prime\, e^+e^-$ mode is constrained
to be $\tau_{\nu^\prime\, e^+e^-} \ge 0.18~(m_{\nu_\tau}/MeV)~sec.$ We point
out that the same experiment implies a similar constraint on the
$\nu^\prime\,\gamma$ mode. This results in a new upper limit on the transition
magnetic moment of $\nu_\tau$, $\mu_{\rm tran} \le 1.1 \times 10^{-9}
(MeV/m_{\nu_\tau})^2 \mu_B $. Furthermore, a limit on the electric charge of
$\nu_\tau$ may be obtained, $Q_{\nu_\tau} \le 4 \times 10^{-4}e$. Combining
these constraints with those arising from supernova observations and primordial
nucleosynthesis calculations, we show that these ``visible'' decays cannot be
the dominant decay modes of the $\tau$ neutrino.
