We examine the linear stability properties of the collisional tearing mode in a reversed-field sheet pinch assuming that the wave vector is not parallel to B, where B is the equilibrium magnetic field. We show that pressure balance in the direction of the equilibrium current requires a nonzero perturbed current component ΔJz that is driven toward tyhe center of the pinch. At the center of the pinch, ΔJz goes to zero, and momentum is balanced by coupling to the ion-acoustic mode. In order to achieve current closure, a large perturbed field-aligned current is generated that is strongly localized about the dissipative tearing layer. The relation of this work to the collisionless case is discussed.