In this paper we consider the multiple access problem with distributed dependent sources. We derive the optimal designs for the case of N correlated binary sources whose data are modelled as a two-state Markov chain. The solution can be classified as a group testing technique where data values at the sensors are determined through the successive refinements of the tests over smaller groups. The tests form, progressively, an accurate map of the sensor data at the central receiver. We derive the conditions on the parameters of the data model for which the group testing approach is superior to time sharing. In contrast to standard multiple access techniques, this is the first method proposed for data retrieval from distributed dependent sources which is content-based rather than user-based.