  We investigate features of the hidden charm-strange scalar tetraquark $c
\overline{c}s\overline{s}$ by calculating its spectral parameters and width,
and we compare the obtained results with the mass and width of the resonance $
X(3960)$ discovered recently in the LHCb experiment. We model the tetraquark as
a diquark-antidiquark state $X=[cs][\overline{c}\overline{s}]$ with
spin-parities $J^{\mathrm{PC}}=0^{++}$. The mass and current coupling of $X$
are calculated using the QCD two-point sum rules by taking into account various
vacuum condensates up to dimension $10$. The width of the tetraquark $X$ is
estimated via the decay channels $X \to D_{s}^{+}D_{s}^{-}$ and $X \to \eta_{c}
\eta^{(\prime)}$. The partial widths of these processes are expressed in terms
of couplings $G$, $g_1$ and $g_2$ which describe the strong interactions of
particles at the vertices $XD_{s}^{+}D_{s}^{-}$, $ X\eta_{c}\eta^{\prime}$ and
$X\eta_{c}\eta$, respectively. Numerical values of $G$, $g_1$ and $g_2$ are
evaluated by employing the three-point sum rule method. Comparing the results
$m=(3976 \pm 85)~\mathrm{MeV}$ and $\Gamma_{ \mathrm{X}}=(42.2 \pm
12.0)~\mathrm{MeV}$ obtained for parameters of the tetraquark $X$ and
experimental data of the LHCb Collaboration, we conclude that the resonance
$X(3960)$ can be considered as a candidate to a scalar diquark-antidiquark
state.
