The mechanisms of exciton generation and recombination in semiconductor nanocrystals are crucial to the understanding of their photophysics and for their application in nearly all fields. While many studies have been focused on type-I heterojunction nanocrystals, the photophysics of type-II nanorods, where the hole is located in the core and the electron is located in the shell of the nanorod, remain largely unexplored. In this work, by scanning single nanorods through the focal spot of radially and azimuthally polarized laser beams and by comparing the measured excitation patterns with a theoretical model, we determine the dimensionality of the excitation transition dipole of single type-II nanorods. Additionally, by recording defocused patterns of the emission of the same particles, we measure their emission transition dipoles. The combination of these techniques allows us to unambiguously deduce the dimensionality and orientation of both excitation and emission transition dipoles of single type-II semiconductor nanorods. The results show that in contrast to previously studied quantum emitters, the particles possess a 3D degenerate excitation and a fixed linear emission transition dipole.