  We derive the field equations and the equations of motion for massive test
particles in modified theories of gravity with an arbitrary coupling between
geometry and matter by using the Palatini formalism. We show that the
independent connection can be expressed as the Levi-Civita connection of an
auxiliary, matter Lagrangian dependent metric, which is related with the
physical metric by means of a conformal transformation. Similarly to the metric
case, the field equations impose the non-conservation of the energy-momentum
tensor. We derive the explicit form of the equations of motion for massive test
particles in the case of a perfect fluid, and the expression of the extra-force
is obtained in terms of the matter-geometry coupling functions and of their
derivatives. Generally, the motion is non-geodesic, and the extra force is
orthogonal to the four-velocity.
