The relativistic complete active-space second-order perturbation theory (CASPT2) is developed for the four-component relativistic Hamiltonian. The present method can describe the near-degenerated and dissociated electronic states of molecules involving atoms of heavy elements. The present approach is less expensive than the relativistic multireference configuration interaction method. The ground and low-lying excited states of TlH, Tl2, and PtH molecules are calculated with the Dirac-Coulomb (DC) CASPT2 method and their spectroscopic constants are obtained. These spectroscopic constants are compared with experimental findings and previous theoretical work. For all the molecules, the spectroscopic constants of DC-CASPT2 show good agreement with the experimental or previous theoretical spectroscopic constants. The present theory provides accurate descriptions of bonding or dissociation states and of ground and excited states in a well-balanced way.