  Current results of the MiniBooNE experiment show excess events that indicate
neutrino oscillations, but only if one goes beyond the standard 3 family
scenario. Recently a different explanation of the events has been given, not in
terms of oscillations but by the production and decay of a massive sterile
neutrino with large transition magnetic moment. We study the effect of such a
sterile neutrino in the rare decays $\tau^- \rightarrow \mu^- \mu^+ \pi^- \nu$
and $\tau^{-}\rightarrow \mu^{-} \mu^{+} e^{-} \nu \nu$. We find that searches
for these decays featuring displaced vertices between the $\mu^-$ and the other
charged particles, constitute good tests for the existence of the sterile
neutrino proposed to explain the MiniBooNE anomaly. These searches could be
done with already existing experimental data.
