Synchrotron x-ray total scattering studies of structural changes in rutile VO2 at the metal-insulator transition temperature of 340 K reveal that monoclinic and tetragonal phases of VO2 coexist in equilibrium, as expected for a first-order phase transition. No evidence for any distinct intermediate phase is seen. Unbiased local structure studies of the changes in V-V distances through the phase transition, using reverse Monte Carlo methods, support the idea of phase coexistence and point to the high degree of correlation in the dimerized low-temperature structure. No evidence for short-range V-V correlations that would be suggestive of local dimers is found in the metallic phase.