Azimuthal and radial polarization states of light are used to produce conical diffraction (CD) from a KGd(WO4)2 crystal. The patterns produced in the ring plane in each case display marked differences than those seen when linearly polarized incident light is used, with the production of a splitting of the CD ring into two concentric rings of equal intensity. The free space evolution for each type of polarization state is also experimentally recorded and investigated. Comparison with theory shows agreement with the experimentally observed results.