Polarization selectivity of third-order and fifth-order Raman spectroscopies is examined for both isotropic liquids and periodic lattices. Our approach directly applies the symmetry property of the probed system to decompose the polarization tensor elements into independent components. The polarization selectivity predicted by symmetry analysis is rigorous and applicable to higher-order Raman spectroscopy. The different polarization selectivities of isotropic systems and periodic lattices can be used as a signature of the liquid-solid phase transition.