  We study possible contributions of heavy sterile neutrinos $\nu_h$ to the
decays $\tau^-\to e^{\pm}(\mu^{\pm})\pi^{\mp}\pi^-$. From the experimental
upper bounds on their rates we derive new constraints on the $\nu_h-\nu_{\tau}$
mixing in the mass region $140.5{MeV}\leq m_{\nu_h}\leq 1637$ MeV. We discuss
cosmological and astrophysical status of $\nu_h$ in this mass region and
compare our constraints with those recently derived by the NOMAD collaboration.
