  We calculate the cross section for $e^+ e^-$ annihilation into $D^{*0} \bar
D^0 +\gamma$ at center-of-mass energies near the $D^{*0} \bar D^{*0}$ threshold
under the assumption that $X(3872)$ is a weakly bound charm meson molecule. The
Dalitz plot has a $\bar D^{*0}$ resonance band in the squared invariant mass
$t$ of $\bar D^0 \gamma$. In the limit as the decay width of the $D^{*0}$ goes
to 0, the Dalitz plot also has a narrow band in the squared invariant mass $u$
of $D^{*0} \bar D^0$ from a charm-meson triangle singularity. At the physical
value of the $D^{*0}$ width, the narrow band reduces to a shoulder. Thus the
triangle singularity cannot be observed directly as a peak in a differential
cross section as a function of $u$. It may however be observed indirectly as a
local minimum in the $t$ distribution for events with $u$ below the triangle
singularity. The minimum is produced by the Schmid cancellation between
triangle loop diagrams and a tree diagram. The observation of this minimum
would support the identification of $X(3872)$ as a weakly bound charm meson
molecule.
