  We use the scale of neutrino mass to derive model-independent naturalness
constraints on possible contributions to muon decay Michel parameters from new
physics above the electroweak symmetry-breaking scale. Focusing on Dirac
neutrinos, we obtain a complete basis of effective dimension four and dimension
six operators that are invariant under the gauge symmetry of the Standard Model
and that contribute to both muon decay and neutrino mass. We show that -- in
the absence of fine tuning -- the most stringent bounds on chirality-changing
operators relevant to muon decay arise from one-loop contributions to neutrino
mass. The bounds we obtain on their contributions to the Michel parameters are
four or more orders of magnitude stronger than bounds previously obtained in
the literature. We also show that there exist chirality-changing operators that
contribute to muon decay but whose flavor structure allows them to evade
neutrino mass naturalness bounds. We discuss the implications of our analysis
for the interpretation of muon decay experiments.
