Complementary resistive switches (CRSs) are suggested as an alternative to one-cell memristor memories to decrease leakage currents. However, their sensing is more difficult and complex than one-cell memristor memories. A method has been given for sensing their state using only DC voltages in the literature. However, in this strategy, sensing one of the logic states results in the destruction of the state and the destroyed state must be written again. To the best of our knowledge, a circuit with this sensing strategy does not exist in the literature yet. In this paper, such a circuit employing this method, which is able to read the CRS cells and able to reconstruct their data if the data are destroyed, is given. A new CRS model is also constructed in this paper and used for simulations to verify the operation of the circuit. The circuit is simulated using Simulink. We expect this circuit implementation to find use in the design and testing of CRS cells.