Using multi configurational ab initio methodologies, we compute the potential energy curves (PECs) of the lowest electronic states of the diatomic CsS. These computations are performed using internally contracted multireference interaction configuration including Davidson correction (MRCI+Q) with and without considering spin-orbit effects. The shapes of the PECs are governed by the interactions between the two ionic states, (2)Sigma(+) and (2)Pi, correlating at large internuclear separations (R-csS) to the first ionic dissociation limit and the other electronic states correlating to the three lowest neutral dissociation limits. Computations show the importance of considering a large amount of electron correlation for the accurate description of the PECs and spectroscopy of this molecular system. As expected, these PECs are also strongly affected by the spin-orbit interaction. For the bound states, we report a set of spectroscopic parameters including equilibrium distances, dissociation energies, and vibrational and rotational constants. The effects of spin-orbit-induced changes on these parameters are also discussed. Moreover, we show that the 2(2)Pi state presents a "bowl" potential with a rather flat region extending to large R-csS distances. After being promoted to this state, wavepackets should undergo strong oscillations, similar to those observed by Zewail and co-workers for the NaI molecule. These should provide information on the shape of the PEC for the 2(2)Pi state and also on the couplings between this and the neighboring states.