  The $D {\bar D}^*$ scattering amplitude and the production of the final
states $\pi^+ \pi^- J/\psi$ and $\pi^+ \pi^- \pi^0 J/\psi$ near the $D^0 {\bar
D}^{*0}$ threshold are discussed following the recent suggestion that the
observed peaks X(3872) and X(3875) in the decays $B \to X K$ are due to a
virtual state $X$ in the $D^0 {\bar D}^{*0}$ channel. The strong interaction is
treated using the small interaction radius approximation. It is shown that the
mass difference between the charged and neutral $D^{(*)}$ mesons results in a
distinctive behavior of the relevant isotopic amplitudes. In particular, the
shape of the peak in the $\pi^+ \pi^- J/\psi$ channel should be significantly
narrower than in the $\pi^+ \pi^- \pi^0 J/\psi$ channel, which property can be
used for an experimental test of the virtual state hypothesis.
