The duality relation for multispin correlation functions of the Potts model on a plane graph is derived using the formulation of a percolation average. It is shown that in simple cases the correlation functions are related to those of the dual graph. But more generally the correlation functions are expressible as linear combinations of ratios of certain percolation averages, the dual partitioned equivalent transmissivities, and dual correlation functions. An overall multiplication factor arises in these considerations, and the author elucidate the graph-theoretic meaning of this function.