An exclusive measurement of the dd -> 3He n pi 0 reaction was carried at a beam momentum of p = 1.2 GeV/c using the WASA-at-COSY facility. For the first time data on the total cross section as well as differential distributions were obtained. The data are described with a phenomenological approach based on a combination of a quasi-free model and a partial wave expansion for three-body reaction. The total cross section is found to be sigma(tot) = (2.89 +- 0.01(stat) +- 0.06(sys) +- 0.29(norm)) mu b. The contribution of the quasi-free processes (with the neutron being target or beam spectator) accounts for 38% of the total cross section and dominates the differential distributions in specific regions of the phase space. The remaining part of the cross section can be described within a partial wave decomposition indicating the significance of p-wave contributions in the final state.