Localized states in an anisotropic single GaAs quantum ring were investigated in terms of polarization dependence of micro-photoluminescence spectrum at 5K. Given four Stokes parameters measured with a pair of linear polarizers and waveplates, the elliptical polarization states of two different vertical confinement states (k=1 and k=2) were compared with phase, rotation, and ellipticity angles. While the polarized emission intensity of the k=2 states becomes enhanced along [1,1,0] compared to that along [1,1¯,0], the polarization asymmetry of the k=1 states shows the opposite result. We conclude the polarization state is determined by the shape of the lateral wavefunctions. In the k=2 state, crescent-like wavefunctions are strongly localized, but the k=1 state consists of two crescent-like wavefunctions, which are connected weakly through quantum tunneling.