An analytic expression for the resolution-broadened neutron scattering function of two-dimensional translational diffusion for polycrystalline samples is derived. We show that this expression exhibits a typical behaviour as a function of the energy resolution width, which can be used in order to distinguish between two- and three-dimensional diffusion. Using experimental data of the protonic conductor, CsOH . H2O, and numerical calculations, it is demonstrated to what extent such an analysis can yield information on the question of dimensionality, which otherwise would only be obtainable from the study of single-crystalline specimens.