  Deviations from Lorentz and CPT invariance in the neutrino sector and their
observable effects in double beta decay are studied. For two-neutrino double
beta decay, a spectral distortion and its properties are characterized for
different isotopes. Majorana couplings for Lorentz violation are studied and
shown to trigger neutrinoless double beta decay even for negligible Majorana
mass. Existing data are used to obtain first limits of $5 \times 10^{-9}$ for
18 individual coefficients and attainable sensitivities in current and future
experiments are presented.
