Non-separable superpositions of polarization and spatial mode of a single photon produce a state that has a polarization that depends on the transverse position, and contains all states of polarization represented on the Poincaré sphere. We have done measurements of the space-dependent state of polarization of single photons prepared in distinct 2×2 (qubit-qubit) and 2×3 (qubit-qutrit) non-separable superpositions of Laguerre-Gauss spatial and polarization states. Detection was done by polarimetry of the light projected at distinct locations in the transverse plane. The polarization patterns had a C-point polarization singularity (lemon, star or monstar) at the center of the transverse wavefunction.