  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 $\mu^+ \to e^+ \bar\nu_e \nu_\ell$ would modify the
neutrino production processes of these experiments. Since $SU(2)_L$ 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 $\mu \to 3e$,
muonium-antimuonium conversion and $\tau \to \mu e e$ rule out any observable
effect for the present experiments due to $\mu^+ \to e^+ \bar\nu_e \nu_\ell$
for $\ell=e,\mu,\tau$, 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.
