A three-dimensional imaging technique installed at the Heidelberg Test Storage Ring (TSR) has been used to investigate the three-body breakup channels occurring in the dissociative recombination process of the methylene ion CH2+. By selecting dissociation planes perpendicular to the molecular beam direction the dissociation kinematics could be measured with unprecedented momentum resolution. Release energies, the relative branching ratio, and the kinematical correlations between the three fragments were determined for the two energetically allowed channels: C(3P)+H(2S)+H(2S) and C(1D)+H(2S)+H(2S).