Exclusive and kinematically complete measurements of the double pionic fusion to $^3$He have been performed in the energy region of the so-called ABC effect, which denotes a pronounced low-mass enhancement in the $pipi$-invariant mass spectrum. The experiments were carried out with the WASA detector setup at COSY. Similar to the observations in the basic $pn to d pi^0pi^0$ reaction and in the $dd to ^4$He$pi^0pi^0$ reaction, the data reveal a correlation between the ABC effect and a resonance-like energy dependence in the total cross section. Differential cross sections are well described by the hypothesis of $d^*$ resonance formation during the reaction process in addition to the conventional $t$-channel $DeltaDelta$ mechanism. The deduced $d^*$ resonance width can be understood from collision broadening due to Fermi motion of the nucleons in initial and final nuclei.