In this paper we address the problem of Distributed Compressed Sensing (DCS) of correlated signals. We model the correlation using the sparse components correlation coefficient of signals, a general and simple measure. We develop an sparse Bayesian learning method for this setting, that can be applied to both random and optimized projection matrices. As a result, we obtain a reduction of the number of measurements needed for a given recovery error that is dependent on the correlation coefficient, as shown by computer simulations in different scenarios.