In legacy networks, overlay multicast protocols are stateless multicast relying on unicast with IP addresses regarding multicast routing states on routers, and thus they offer cost-effectiveness and robustness. Wireless sensor networks (WSNs) consist of a large number of randomly deployed sensors with unattended batteries and constrained device capabilities. For non-uniform and resource-sensitive WSNs multicast protocols also have taken an overlay approach. The protocols establish a cost-optimal structure, a Steiner tree, among destinations as an overlay structure and exploit geographic routing for unicasting. However, such concentration on the Steiner tree structure may paradoxically burden the irregular and resource-constrained WSNs with heavy loads for heuristic structure construction and fault-tolerant maintenance. In addition, it leads to frequent tree reconstruction, thus it could harm data multicast transmission seriously. Regarding these problems, we consider a proxy district per a destination for overlay tree formation to prevent structural dynamic alteration and support local state management. This district-based overlay multicast might be able to keep the stateless advantages of traditional overlay multicast. By overhead analysis and various computational simulations, we prove that our proposal provides robust and efficient multicast transmission