If the atmospheric and the solar neutrino problem are both explained by neutrino oscillations, and if there are only three light neutrinos, then all mass-squared differences between the neutrinos are known. In such a case, existing terrestrial neutrino oscillation experiments cannot be significantly affected by neutrino oscillations, but, in principle there could be an anomaly in the neutrino flux due to new neutrino interactions. We discuss how a non-standard muon decay mu(sup+) --> e(sup+)anti-nu(sub e)nu(sub l) would modify the neutrino production processes of these experiments. Since SU(2)(sub L) violation is small for New Physics above the weak scale one can use related flavor-violating charged lepton processes to constrain these decays in a model independent way. We show that the upper bounds on mu --> 3e, muonium-antimuonium conversion and tau --> mu e e rule out any observable effect for the present experiments due to mu(sup+) --> e(sup+) n u(sub e)nu(sub l) for l= e, mu, tau respectively. Applying similar arguments to flavor-changing semi-leptonic reactions we exclude the possibility that the 'oscillation signals' observed at LSND are due to flavor-changing interactions that conserve total lepton number.
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