  We have conducted a study of the femtoscopic correlation functions for the
$D^0D^{*+}$ and $D^+D^{*0}$ channels that build the $T_{cc}$ state. We develop
a formalism that allows us to factorize the scattering amplitudes outside the
integrals in the formulas, and the integrals involve the range of the strong
interaction explicitly. For a source of size of 1 fm, we find values for the
correlation functions of the $D^0 D^{*+}$ and $D^+D^{*0}$ channels at the
origin around 30 and 2.5, respectively, and we see these observables converging
to unity already for relative momenta of the order of 200 MeV. We conduct tests
to see the relevance of the different contributions to the correlation function
and find that it mostly provides information on the scattering length, since
the presence of the source function in the correlation function introduces an
effective cut in the loop integrals that makes them quite insensitive to the
range of the interaction.
