The diffusion of a tracer gas from a plane, porous boundary into a steady, rarefied background is investigated using the BGK model to account for collisions between the tracer and the background molecules. In a limited region close to the central part of the wall the diffusion process is nearly one-dimensional, and the resulting kinetic diffusion equation is shown to be identical to the shear flow equation in the Kramers problem of flow along an infinite wall. This observation suggests that density measurements, rather than measurements of velocity, can be used to assess the validity of the linearized BGK model in describing flows in kinetic boundary layers. Estimates of the required sensitivity of the experimental technique are given.