Series-Series (SS) and Series-Parallel (SP) topologies are widely utilized in practical resonant inductive coupling wireless power transfer (RIC-WPT) systems owing to their simple circuit configurations. Conventionally, design optimization of the circuit parameters of these topologies were investigated separately, because these topologies are expressed by different equivalent circuits. However, analysis of these equivalent circuits is generally complicated due to the multiple resonant modes contained in the operation, which may cause difficulty in comparing the performance between the SS and SP topologies after design optimization of these topologies. This difficulty may prevent elucidating the methodology to select an appropriate topology that offers better output power or efficiency after design optimization. The purpose of this paper is to suggest a selection methodology of the SS and SP topologies by elucidating a novel insight that these topologies have the quasi-duality relation, in which the SP topology works approximately as the dual of the SS topology. This insight enables to share the analysis results between the topologies. As a result, both of these topologies were found to be expressed by a same novel equivalent circuit. Furthermore, the only difference between the SS and SP topologies were found to be the equivalent load resistance of this equivalent circuit, thus reducing the topology selection into selection of preferable load resistance. The appropriateness of the quasi-duality relation and the resultant equivalent circuit was successfully confirmed by the simulation and the experiment.