  It is pointed out that the internal structure of the narrow resonance X(3872)
at the D^0 {\bar D}^{*0} threshold can be studied in some detail by measuring
the rate and the spectra in the decays X(3872) \to D^0 {\bar D}^0 \pi^0 and
X(3872) \to D^0 {\bar D}^0 \gamma. In particular, if this resonance contains a
dominant `molecular' component D {\bar D^*} \pm {\bar D} D^*, this component
can be revealed and studied by a distinct pattern of interference between the
underlying decays of D^{*0} and {\bar D}^{*0} whose coherence is ensured by
fixed (but yet unknown) C parity of the X(3872).
