  Exclusive measurements of the quasi-free $np \to np\pi^0\pi^0$ reaction have
been performed by means of $dp$ collisions at $T_d$ = 2.27 GeV using the WASA
detector setup at COSY. Total and differential cross sections have been
obtained covering the energy region $\sqrt s$ = (2.35 - 2.46) GeV, which
includes the region of the ABC effect and its associated $d^*(2380)$ resonance.
Adding the $d^*$ resonance amplitude to that for the conventional processes
leads to a reasonable description of the data. The observed resonance effect in
the total cross section is in agreement with the predictions of F\"aldt and
Wilkin as well Albadajedo and Oset. The ABC effect, {\it i.e.} the low-mass
enhancement in the $\pi^0\pi^0$-invariant mass spectrum, is found to be very
modest - if present at all, which might pose a problem to some of its
interpretations.
