The gravitational properties of the neutrino are studied in the weak-f
ield approximation. By imposing the Hermiticity condition, CPT, and CP
invariance on the energy-momentum tensor matrix element, we show that
the allowed gravitational form factors for Dirac and Majorana neutrin
os are very different. In a CPT- and CP-invariant theory, the energy-m
omentum tensor for a Dirac neutrino of the same species is characteriz
ed by four gravitational form factors. As a result of CPT invariance,
the energy-momentum tensor for a Majorana neutrino of the same species
has five form factors. In a CP-invariant theory, if the initial and f
inal Majorana neutrinos have the same (opposite) CP parity, then only
tensor(pseudotensor)-type transitions are allowed.