A quantum theory on angular momentum coupling in pre-dissociation processes of triatomic molecules is presented. The initially prepared state of an asymmetric top is first resolved into state vectors in the recoil frame by an addition theorem of spherical harmonics. Under the influence of an anisotropic, repulsive potential, the evolution of the predissociative density matrix determines the subsequent angular momentum coupling between photofragments, including their interfragmental orbital angular momentum. The present framework provides a foundation to tackle the problem of pair-correlated angular distributions of photofragments from pre-dissociations of polyatomic molecules.