This paper is concerned with optimal estimation of the state of a Boolean dynamical systems observed through correlated noisy Boolean measurements. The optimal Minimum Mean-Square Error (MMSE) state estimator for general Partially-Observed Boolean Dynamical Systems (POBDS) can be computed via the Boolean Kalman Filter (BKF). However, thus far in the literature only the case of white observation noise has been considered. In this paper, we develop the optimal MMSE filter for a class of POBDS with correlated Boolean measurements. The performance of the proposed method is subsequently investigated using the p53-MDM2 negative feedback loop genetic network model.