  The gravitational properties of the neutrino is studied in the weak field
approximation. By imposing the hermiticity condition, CPT and CP invariance on
the \em tensor matrix element, we shown that the allowed gravitational form
factors for Dirac and Majorana neutrinos are very different. In a CPT and CP
invariant theory, the \em tensor for a Dirac neutrino of the same specie is
characterized by four gravitational form factors. As a result of CPT
invariance, the \em tensor for a Majorana neutrino of the same specie has five
form factors. In a CP invariant theory, if the initial and final Majorana
neutrinos have the same (opposite) CP parity, then only tensor (pseudo-tensor)
type transition are allowed.
