  We investigate the dynamics of spin-$\tfrac{1}{2}$ particles that are freely
propagating in superposed states in curved spacetime. We first make use of a
Wentzel-Kramers-Brillouin approximation of the Dirac equation in curved
spacetime to extract the corresponding Mathisson-Papapetrou-Dixon equations
that describe the deviation from geodesic motion as well as the spin precession
of such particles. We then discuss, in light of our results, the case of
flavour neutrinos which are, by nature, a superposition of mass eigenstates.
