A comprehensive study of the local and nonlocal amplitudes contributing to the decay B0 → K0(→ K+π−)μ+μ− is performed by analysing the phase-space distribution of the decay products. The analysis is based on pp collision data corresponding to an integrated luminosity of 8.4 fb−1 collected by the LHCb experiment. This measurement employs for the first time a model of both one-particle and two-particle nonlocal amplitudes, and utilises the complete dimuon mass spectrum without any veto regions around the narrow charmonium resonances. In this way it is possible to explicitly isolate the local and nonlocal contributions and capture the interference between them. The results show that interference with nonlocal contributions, although larger than predicted, only has a minor impact on the Wilson Coefficients determined from the fit to the data. For the local contributions, the Wilson Coefficient C9, responsible for vector dimuon currents, exhibits a 2.1σ deviation from the Standard Model expectation. The Wilson Coefficients C10, C9′ and C10′ are all in better agreement than C9 with the Standard Model and the global significance is at the level of 1.5σ. The model used also accounts for nonlocal contributions from B0→ K0[τ+τ−→ μ+μ−] rescattering, resulting in the first direct measurement of the bsττ vector effective-coupling C9τ.