A crossed beam study of the quenching of NH(a 1∆) molecules by the collision partners Xe and CO is presented. Relative cross sections for the formation of the various rovibrational/fine-structure states in the NH(X 3∑-) products are reported. Vibrational levels v=0-4 were detected, and the vibrational state distribution was found to be monotonically decreasing with increasing v. Despite the large energy gap, the rotational state distribution was found to be quite cold. Population in all three fine-structure levels of a given rotational angular momentum N was found, and the distributions among the fine-structure levels were nearly statistical. The observed fine-structure state distribution differs significantly from that observed for the spin-forbidden decomposition of HN3, for which no significant population in the F2 levels was observed. These experimental results are interpreted with a heuristic model in which the collision-induced spin-orbit coupling which enables the mixing of the initial singlet and final triplet states is derived by consideration of the polarization of the NH electronic wave functions induced by the approach of the collision partner.