  In this article, we construct the $C \otimes \gamma_\mu C$ and $C\gamma_5
\otimes \gamma_5\gamma_\mu C$ type currents to interpolate the vector
tetraquark states, then carry out the operator product expansion up to the
vacuum condensates of dimension-10 in a consistent way, and obtain four QCD sum
rules. In calculations, we use the formula
$\mu=\sqrt{M^2_{Y}-(2{\mathbb{M}}_c)^2}$ to determine the optimal energy scales
of the QCD spectral densities, moreover, we take the experimental values of the
masses of the $Y(4260/4220)$, $Y(4360/4320)$, $Y(4390)$ and $Y(4660/4630)$ as
input parameters and fit the pole residues to reproduce the correlation
functions at the QCD side. The numerical results support assigning the
$Y(4660/4630)$ to be the $C \otimes \gamma_\mu C$ type vector tetraquark state
$c\bar{c}s\bar{s}$, assigning the $Y(4360/4320)$ to be $C\gamma_5 \otimes
\gamma_5\gamma_\mu C$ type vector tetraquark state $c\bar{c}q\bar{q}$, and
disfavor assigning the $Y(4260/4220)$ and $Y(4390)$ to be the pure vector
tetraquark states.
