  We study the non-relativistic limit of Dirac equation for mixed neutrinos. We
demonstrate that such a procedure inevitably leads to a redefinition of the
inertial mass. This happens because, in contrast to the case when mixing is
absent, the antiparticle sector contribution cannot be neglected for neutrinos
with definite flavor. We then show that, when a gravitational interaction is
switched on, in the weak-field approximation the mass parameter which couples
to gravity (gravitational mass) does not undergo the same reformulation as the
inertial mass, thus leading to an apparent breakdown of the weak equivalence
principle.
