This paper considers a diffusion-based molecular communication system where the transmitter uses Reaction Shift Keying (RSK) as the modulation scheme. We focus on the demodulation of RSK signal at the receiver. The receiver consists of a front-end molecular circuit and a back-end demodulator. The front-end molecular circuit is a set of chemical reactions consisting of multiple chemical species. The optimal demodulator computes the posteriori probability of the transmitted symbols given the history of the observation. The derivation of the optimal demodulator requires the solution to a specific Bayesian filtering problem. The solution to this Bayesian filtering problem had been derived for a few specific molecular circuits and specific choice(s) of observed chemical species. The derivation of such solution is also lengthy. The key contribution of this paper is to present a general solution to this Bayesian filtering problem which can be applied to any molecular circuit and any choice of observed species.