The rotational state distributions of NO molecules scattered at clean and oxidized Ge surfaces were determined by means of laser induced fluorescence (LIF). For low incident kinetic energies (Ekin ≲ 200 meV) scattering is dominated by trapping/desorption and the molecules coming off the surface are translationally accommodated to the surface temperature. The rotational state populations can in this case be approximated by a Boltzmann distribution. The rotational temperature Trot equals the surface temperature Ts, however only up to about 250 K. Further increase of Ts leads to a leveling off of Trot until a limiting value Trot,lim ≈400 K is reached. (Rotational cooling in desorption.) At higher kinetic energies direct-inelastic scattering dominates, and for E kin=820 meV a pronounced non-Boltzmann distribution (rotational rainbow) is observed. The observed effects are qualitatively interpreted in terms of current theoretical models.