  Matrix element $U_{\tau N}$ of sterile neutrino N mixing with $\nu_{\tau}$ is
the least constrained in the literature among the three $U_{\alpha N}$
($\alpha=e,\mu,\tau$) mixing parameters characterizing the sterile neutrino
phenomenology. We study the contribution of massive dominantly sterile
neutrinos to purely leptonic $\tau$-decays and semileptonic decays of $\tau$
and K, D mesons. We consider some decays allowed in the Standard Model (SM) as
well as Lepton Flavor and Lepton Number Violating (LFV, LNV) decays forbidden
in the SM. From the existing experimental data on the branching ratios of these
processes we derived new limits on $U_{\tau N}$ more stringent than the ones
existing in the literature. These limits are extracted in a model independent
way without any ad hoc assumptions on the relative size of the three different
sterile neutrino mixing parameters.
