Conical intersections between Born-Oppenheimer potential energy surfaces create singularities which are known to have a direct effect on the symmetry of the nuclear wave functions. In this article is presented a quasi-Jahn-Teller model to study the symmetry effects of these singularities on nonreactive and reactive scattering processes. Applying this model, we were able to determine in what way and to what extent the conical intersection affects the relevant S-matrix elements. Having the results of this study available, conclusions concerning more realistic systems were derived.