We consider the hypothesis that neutrino oscillation data can be expla
ined if the gravitational couplings of (massless or degenerate mass) n
eutrinos are flavor nondiagonal, in violation of the equivalence princ
iple. We analyze the various neutrino oscillation laboratory experimen
tal data including the recent LSND observations to constrain the relev
ant parameter space. We find (under the hypothesis that gravity couple
s to matter and antimatter in the same way) that there is no allowed r
egion of parameter space which can explain the existing data, implying
that the LSND result cannot be explained by oscillations of degenerat
e-mass neutrinos due to equivalence principle violations.