As the integration of a high proportion distributed generation (DG) into the power grid increases, topological changes in the distribution network become more frequent. A method for the topological identification in the distribution network based on the random forest (RF) and the maximal information coefficient (MIC) for key feature selection is proposed to address the issues of high measurement feature requirements and low identification accuracy in that identification for such networks containing DG. First, considering the uncertainty and correlation of wind and solar power output, typical scenarios of wind and solar power output are obtained based on the Frank-Copula function, and combined with different distribution network topologies to construct a dataset. Then, feature selection is performed using RF and MIC to identify the most important and key non-redundant features for topological identification. Finally, the bat algorithm (BA) is employed to optimize a back propagation (BP) neural network model for identification. Simulation analyses are conducted on the IEEE33 and the PG&E69-bus distribution networks to validate the feasibility of the proposed model.