Whereas atom-molecule collisions have been studied with complete quantum-state resolution, interactions between two state-selected molecules have proven much harder to probe. Here, we report the measurement of state-resolved inelastic scattering cross sections for collisions between two open-shell molecules that are both prepared in a single quantum state. Stark-decelerated hydroxyl (OH) radicals were scattered with hexapole-focused nitric oxide (NO) radicals in a crossed-beam configuration. Rotationally and spin-orbit inelastic scattering cross sections were measured on an absolute scale for collision energies between 70 and 300 cm(-1). These cross sections show fair agreement with quantum coupled-channels calculations using a set of coupled model potential energy surfaces based on ab initio calculations for the long-range nonadiabatic interactions and a simplistic short-range interaction. This comparison reveals the crucial role of electrostatic forces in complex molecular collision processes.