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We perform a unitary coupled channel study of the interaction of the $D^{*+}D^0, D^{*0} D^+$ channels and find a state barely bound, very close to isospin$I=0$. We take the experimental mass as input and obtain the width of the stateand the $D^0 D^0 \pi^+$ mass distribution. When the mass of the $T_{cc}$ statequoted in the experimental paper from raw data is used, the width obtained isof the order of the $80 \;{\rm keV}$, small compared to the value given in thatwork. Yet, when the mass obtained in an analysis of the data considering theexperimental resolution is taken, the width obtained is about $43 \;{\rm keV}$and both the width and the $D^0 D^0 \pi^+$ mass distribution are in remarkableagreement with the results obtained in that latter analysis.

$D^0 D^0 \pi^+$ mass distribution in the production of the $T_{cc}$ exotic state