  We consider Schr\"odinger operators on possibly noncompact Riemannian
manifolds, acting on sections in vector bundles, with locally square integrable
potentials whose negative part is in the underlying Kato class. Using path
integral methods, we prove that under geodesic completeness these differential
operators are essentially self-adjoint on the space of smooth functions with
compact support, and that the corresponding operator closures are semibounded
from below. These results apply to nonrelativistic Pauli-Dirac operators that
describe the energy of Hydrogen type atoms on Riemannian 3-manifolds.
