The cooperative output regulation problem for singular multi-agent systems subject to static networks was studied recently under the assumption that each follower system satisfies the standard assumption. In this paper, we further study the same problem for singular multi-agent systems subject to jointly connected switching networks. First, by introducing a static output feedback control, we remove the unnecessary standard assumption on the singular system in the existing result. Then, we derive a reduced-order normal multi-agent system and obtain a distributed output measurement feedback control law based on the existing result on the normal multi-agent system. Finally, we show that the composition of the static output feedback control law and the distributed output measurement feedback control law solves the cooperative output regulation problem for the original singular multi-agent system. Our result enlarges the class of systems whose cooperative output regulation problem is solvable.