The search for He4-η bound states was performed with the WASA-at-COSY facility via the measurement of the excitation function for the dd→He3nπ0 and dd→He3pπ− processes. The deuteron beam momentum was varied continuously between 2.127 GeV/c and 2.422 GeV/c, corresponding to the excess energy for the dd→He4η reaction ranging from Q=−70 MeV to Q=30 MeV. The luminosity was determined based on the dd→He3n reaction and the quasi-free proton–proton scattering via dd→ppnspectatornspectator reactions. The excitation functions, determined independently for the measured reactions, do not reveal a structure which could be interpreted as a narrow mesic nucleus. Therefore, the upper limits of the total cross sections for the bound state production and decay in dd→(He4-η)bound→He3nπ0 and dd→(He4-η)bound→He3pπ− processes were determined taking into account the isospin relation between the both of the considered channels. The results of the analysis depend on the assumptions of the N⁎(1535) momentum distribution in the anticipated mesic-He4. Assuming, as in the previous works, that this is identical with the distribution of nucleons bound with 20 MeV in He4, we determined that (for the mesic bound state width in the range from 5 MeV to 50 MeV) the upper limits at 90% confidence level are about 3 nb and about 6 nb for nπ0 and pπ− channels, respectively. However, based on the recent theoretical findings of the N⁎(1535) momentum distribution in the N⁎-He3 nucleus bound by 3.6 MeV, we find that the WASA-at-COSY detector acceptance decreases and hence the corresponding upper limits are 5 nb and 10 nb for nπ0 and pπ− channels respectively.