A search for time-integrated CP violation in the Cabibbo-suppressed decay D0→π+π−π+π− is performed using an unbinned, model-independent technique known as the energy test. This is the first application of the energy test in four-body decays. The search is performed for P-even CP asymmetries and, for the first time, is extended to probe the P -odd case. Using proton–proton collision data corresponding to an integrated luminosity of 3.0 fb−1 collected by the LHCb detector at centre-of-mass energies of View the MathML source and 8 TeV, the world's best sensitivity to CP violation in this decay is obtained. The data are found to be consistent with the hypothesis of CP symmetry with a p -value of (4.6±0.5)% in the P-even case, and marginally consistent with a p -value of (0.6±0.2)% in the P-odd case, corresponding to a significance for CP non-conservation of 2.7 standard deviations.