We demonstrate that combining two independently tunable vacuum ultraviolet (VUV) lasers and the time-slice velocity-map-imaging-photoion (VMI-PI) method allows the rovibronically state-selected photodissociation study of CO in the VUV region along with the state-selective detection of product C((3)P(0,1,2)) using the VUV-UV (1+1') resonance-enhanced photoionization and the VUV Rydberg autoionization methods. Both tunable VUV lasers are generated based on the two-photon resonance-enhanced four-wave mixing scheme using a pulsed rare gas jet as the nonlinear medium. The observed fine-structure distributions of product C((3)P(J)), J = 0, 1, and 2, are found to depend on the CO rovibronic state populated by VUV photoexcitation. The branching ratios for C((3)P0) + O((3)P(J)): C((3)P0) + O((1)D2), C((3)P1) + O((3)P(J)): C((3)P1) + O((1)D2), and C((3)P2) + O((3)PJ): C((3)P2) + O((1)D2), which were determined based on the time-slice VMI-PI measurements of C(+) ions formed by J-state selective photoionization sampling of C((3)P(0,1,2)), also reveal strong dependences on the spin-orbit state of C((3)P(0,1,2)). By combining the measured branching ratios and fine-structure distributions of C((3)P(0,1,2)), we have determined the correlated distributions of C((3)P(0,1,2)) accompanying the formation of O((1)D2) and O((3)P(J)) produced in the VUV photodissociation of CO. The success of this demonstration experiment shows that the VUV photodissociation pump-VUV photoionization probe method is promising for state-to-state photodissociation studies of many small molecules, which are relevant to planetary atmospheres as well as fundamental understanding of photodissociation dynamics.