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 d
irectional 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.
