[en] We present a new determination of the parity of the neutral pion via the double Dalitz decay π⁰→e⁺e^-e⁺e^-. Our sample, which consists of 30 511 candidate decays, was collected from K_L→π⁰π⁰π⁰ decays in flight at the KTeV-E799 experiment at Fermi National Accelerator Laboratory. We confirm the negative π⁰ parity and place a limit on scalar contributions to the π⁰→e⁺e^-e⁺e^- decay amplitude of less than 3.3% assuming CPT conservation. The π⁰γ*γ* form factor is well described by a momentum-dependent model with a slope parameter fit to the final state phase-space distribution. Additionally, we have measured the branching ratio of this mode to be B(π⁰→e⁺e^-e⁺e^-)=(3.26±0.18)x10^-5