We show that polarimetry of H emission in sunpernova remnant shocks can be a powerful diagnostic of cosmic-ray modified shocks (CRMSs). Solving the radiative line transfer problem for collisionless shocks propagating into a partially ionized medium, we find the directions of the linearly polarized H strongly dependent on the existence of shock modification; the direction is parallel to the direction of shock travel for the case of the CRMS, while the direction is perpendicular for the case of no modification.