We investigate theoretically dark resonance spectroscopy for a dilute atomic vapor confined in a thin (micro-metric) cell. We identify the physical parameters characterizing the spectra and study their influence. We focus on a Hanle-type situation, with an optical irradiation under normal incidence and resonant with the atomic transition. The dark resonance spectrum is predicted to combine broad wings with a sharp maximum at line-center, that can be singled out when detecting a derivative of the dark resonance spectrum. This narrow signal derivative, shown to broaden only sub-linearly with the cell length, is a signature of the contribution of atoms slow enough to fly between the cell windows in a time as long as the characteristic ground state optical pumping time. We suggest that this dark resonance spectroscopy in micro-metric thin cells could be a suitable tool for probing the effective velocity distribution in the thin cell arising from the atomic desorption processes, and notably to identify the limiting factors affecting desorption under a grazing incidence.