Six-dimensional quantum dynamical calculations are presented for the reaction of (v,j) H-2 on Cu(100), at normal incidence, for v=0-1 and j=0-5. The dynamical calculations employed a potential energy surface computed with density functional theory, using the generalized gradient approximation and a slab representation for the adsorbate-substrate system. The aim of the calculations was to establish signatures from which experiments could determine the dominant reaction site of H-2 on the surface and the dependence of the reaction site on the initial rovibrational state of H-2. Two types of signatures were found. First, we predict that, at energies near threshold, the reaction of (v=1) H-2 is rotationally enhanced, because it takes place at the top site, which has an especially late barrier and a reaction path with a high curvature. On the other hand, we predict the reaction to be almost independent of j for (v=0) H-2, which reacts at the bridge site. Second, we predict that, at collision energies slightly above threshold for which the reaction probabilities of the (v=0) and (v=1) states are comparable, the rotational quadrupole alignment of (v=1) reacting molecules should be larger than that of (v=0) reacting molecules, for j=1, 4, and 5. For (j=2) H-2, the opposite should be true, and for (j=3) H-2, the rotational quadrupole alignment should be approximately equal for (v=1) and (v=0) H-2. These differences can all be explained by the difference in the predicted reaction site for (v=1) and (v=0) H-2 (top and bridge) and by the differences in the anisotropy of the potential at the reaction barrier geometries associated with these sites. Our predictions can be tested in associative desorption experiments, using currently available experimental techniques.