This letter reports a first quantitative analysis of the contribution of higher partial waves in the charge symmetry breaking reaction $dd to {}^4text{He}pi^0$ using the WASA-at-COSY detector setup at an excess energy of $Q = 60$ MeV. The determined differential cross section can be parametrized as $text{d}sigma/text{d}Omega = a + bcos^{2}theta^*$, where $theta^*$ is the production angle of the pion in the center-of-mass coordinate system, and the results for the parameters are $a = left(1.55 pm 0.46 (text{stat}) ^{+0.32}_{-0.8} (text{syst}) right)$ pb/sr and $b = left(13.1 pm 2.1 (text{stat}) ^{+1.0}_{-2.7} (text{syst})right)$ pb/sr. The data are compatible with vanishing p-waves and a sizable d-wave contribution. This finding should strongly constrain the contribution of the $Delta$ isobar to the $dd to {}^4text{He}pi^0$ reaction and is, therefore, crucial for a quantitative understanding of quark mass effects in nuclear production reactions.