  We generalize the formalism for testing Lorentz invariance and the
equivalence principle in the neutrino sector. While neutrino oscillation bounds
constrain the region of large mixing of the the weak and gravitational
eigenstates, we obtain new constraints on violations of Lorentz invariance and
the equivalence principle from neutrinoless double beta decay. These bounds
apply even in the case of no mixing and thus probe a totally unconstrained
region in the parameter space.
