X(3872) diagnostics with decays to D {\bar D} \gamma

It is pointed out that in the decays $X(3872) \to D {\bar D} \gamma$ the possible `molecular' component of the X(3872) should give rise essentially only to a $D^0 {\bar D}^0 \gamma$ final state with a predictable spectrum, and should yield virtually no contribution to decays into $D^+D^- \gamma$. The latter final state with charged $D$ mesons should however arise from the radiative decays of the short-distance core of the X(3872) through the transition $X(3872) \to \psi(3770) \gamma$. Thus an observation of the radiative decays of X(3872) to pairs of neutral and charged $D$ mesons would provide an insight into the internal dynamics of the X(3872) resonance.