We investigate the possible effect of cascade transitions from the (4s5p) 3 P0,1,2 states to the (4s5s) 3 S1 state of Zn. The polarization of the light emitted in the subsequent decay to the (4s4p) 3 P0,1,2 states has been the subject of recent controversy, with significant disagreement between the experimental data reported by Pravica et al. (Phys. Rev. A 83 (2011) 040701) and by Clayburn and Gay (Phys. Rev. Lett. 119 (2017) 093401) in the cascade-free region below ≈ 7.6 eV incident energy and relatively good agreement above. The cross sections for excitation of the (4s5p) 3 P0,1,2 states, as well as higher-lying triplet states, and the linear polarization of the cascade radiation seem too small to produce a significant alignment of the (4s5s) 3 S1 state, thereby raising additional questions regarding the origin of the relatively large linear polarizations measured above the cascade threshold.