  The neutrino oscillations in the field of a rotating deformed mass is
investigated. The phase shift is evaluated in the case of weak field limit,
slow rotation and small deformation. To this aim the Hartle-Thorne metric is
used, which is an approximate solution of the vacuum Einstein equations
accurate to second order in the rotation parameter $a/M$ and to first order in
the mass quadrupole moment $q$. Implications on atmospheric, solar and
astrophysical neutrinos are discussed.
