Not in an isotropic material. Anisotropic materials have permittivities and/or permeabilities that depend upon the orientation of the incident fields. As such, the polarization of the light will affect the apparent index of refraction. Take as an example a birefringent material. You can take a circularly polarized light as being the superposition of two normal linearly polarized waves. So the CP light will behave differently from a LP wave since it will have a component normal to the LP wave. Though this would imply that the transmitted and reflected waves will not preserve circular polarization.