At first sight, the quenched tetragonal spinel CuMn2O4 can be formulated with Cu2+ and Mn3+, implying that the tetrahedral site is Jahn-Teller (JT)-active Cu2+ and the octahedral site is JT-active Mn3+. High-resolution, high-momentum-transfer neutron scattering analysis suggests that the sample has similar to 30% inversion: Mn on the tetrahedral Cu site with compensating Cu on the octahedral site. Reverse Monte Carlo (RMC) analysis of the pair distribution function allows details of metal-oxygen connectivity to be probed in a manner that is significantly on the local rather than the average scale. Bond valence analysis of the RMC supercell reveals that both JT ions disproportionate to higher and lower valence states as a means of avoiding their JT tendency, particularly on the tetrahedral site. The occurrence of Cu3+ in particular is suggested for the first time and is supported by X-ray photoelectron spectroscopy data. The bimodal distribution of O-Cu-O bond angles at the tetrahedral site (distinct from what is seen for O-Mn-O bond angles) further reveals a hidden distinction between sites previously considered to be equivalent. Application of total scattering techniques originally developed for highly disordered materials permits the examination of nanoscale crystalline structure with elemental specificity that is not available in traditional reciprocal-space analysis.