This paper proposes an algorithm, including a multiagent-based system architecture, for distributed inference of power grid topologies. The core algorithm is based on processing measurement time series, or fingerprints, using statistical correlation to determine the connectivity between nodes. Notably, the method and proposed system architecture is completely distributed. The solution has been developed with contemporary IEC 61850 compliant substation automation systems in mind. This paper includes a presentation of the theoretical foundation for the distributed topology inference algorithm as well as the proposed system architecture. A case study utilizing the RBTS bus 4 model is included to demonstrate the capabilities of the method under static as well as transient situations. Furthermore, the results and analysis of the performance and scalability of the algorithm are presented. The main contribution of this paper is an application to infer the electrical connectivity of power grids without central functionality.