A density-functional-theory-based relativistic scattering formalism is used to study charge transport through thin Pt films with room-temperature lattice disorder. A Fuchs-Sondheimer specularity coefficient p∼0.5 is needed to describe the suppression of the charge current at the surface even in the absence of surface roughness. The charge current drives a spin Hall current perpendicular to the surface. Analyzing the latter with a model that is universally used to interpret the spin Hall effect in thin films and layered materials, we are unable to recover values of the spin-flip diffusion length lsf and spin Hall angle ΘsH that we obtain for bulk Pt using the same approximations. We trace this to the boundary conditions used and develop a generalized model that takes surface effects into account. A reduced value of ΘsH at the surface is then found to describe the first-principles transport results extremely well. The in-plane spin Hall effect is substantially enhanced at the surface.