  Whether the $Y(4260)$ can couple to open charm channels has been a crucial
issue for understanding its nature. The available experimental data suggest
that the cross section line shapes of exclusive processes in $e^+e^-$
annihilations have nontrivial structures around the mass region of the
$Y(4260)$. As part of a series of studies of the $Y(4260)$ as mainly a
$\bar{D}D_1(2420)+c.c.$ molecular state, we show that the partial widths of the
$Y(4260)$ to the two-body open charm channels of $e^+e^-\to D^*\bar{D}^*$ and
$D_s^*\bar{D}_s^*$ are much smaller than that to $\bar{D}D^*\pi+c.c.$. The line
shapes measured by the Belle Collaboration for these two channels can be well
described by the vector charmonium states $\psi(4040)$, $\psi(4160)$ and
$\psi(4415)$ together with the $Y(4260)$. It turns out that the interference of
the $Y(4260)$ with the other charmonia produces a dip around 4.22~GeV in the
$e^+e^-\to D^*\bar{D}^*$ cross section line shape. The data also show an
evidence for the strong coupling of the $Y(4260)$ to the $D\bar D_1(2420)$, in
line with the expectation in the hadronic molecular scenario for the $Y(4260)$.

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