Heavy quark spin selection rule and the properties of the X(3872)

The properties of the resonance X(3872) are discussed under the assumption that this resonance is dominantly a `molecular' $J^{PC}=1^{++}$ state of neutral $D$ and $D^*$ mesons. It is argued that in these properties should dominate the states with the total spin of the charmed quark-antiquark pair equal to one. As a practical application of this observation the ratio of the rates of the decays $X \to \pi^0 \chi_{cJ}$ for different $J$ is predicted. It is also pointed out that the total rate of these decays is likely to be comparable to that of the observed transitions $X \to \pi^+ \pi^- J\psi$ and $X \to \pi^+ \pi^- \pi^0 J\psi$. The decays of the X into light hadrons and its production in hadronic processes are also briefly discussed.