  Possibilities to test the Lorentz invariance of the weak interaction in muon
decay are considered. We derive the direction-dependent muon-decay rate with a
general Lorentz-violating addition to the W-boson propagator. We discuss
measurements of the directional and boost dependence of the Michel parameters
and of the muon lifetime as a function of absolute velocity. The total
muon-decay rate in the Lorentz-violating Standard Model Extension is addressed.
Suggestions are made for dedicated (re)analyses of the pertinent data and for
future experiments.
