A search for CP and P violation in charmless four-body B0→pp¯K+π- decays is performed using triple-product asymmetry observables. It is based on proton-proton collision data collected by the LHCb experiment at center-of-mass energies of 7, 8 and 13 TeV, corresponding to a total integrated luminosity of 8.4 fb-1. The CP- and P-violating asymmetries are measured both in the integrated phase space and in specific regions. No evidence is seen for CP violation. P-parity violation is observed at a significance of 5.8 standard deviations.