We theoretically analyze the angular momentum distribution of molecules desorbing from a surface. The adsorbate is shown to possess the complete point symmetry of the surface if the molecules adsorb in statistically equilibrated local order. Considering the symmetry of the angular momentum distribution, this point symmetry adopted to the desorbate is particularly taken into account. From the symmetry analysis, the cancellation of several terms in the angular momentum distribution is concluded. The symmetry related sparseness of the angular momentum distribution strongly simplifies the interpretation of experimental data and thus enables an appropriate comparison between experiment and theory. The benefit of this simplified picture is demonstrated by the example of the laser induced desorption of CO molecules from a Cr2O3(0001) surface. (C) 2003 American Institute of Physics.