We report a study of the decay ${B}_{s}^{0}\ensuremath{\rightarrow}{D}_{s}^{(*)}{D}_{s}^{(*)}$ using a data sample corresponding to $1.3\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of integrated luminosity collected by the D0 experiment in 2002--2006 during run II of the Fermilab Tevatron collider. One ${D}_{s}^{(*)}$ meson was partially reconstructed in the decay ${D}_{s}\ensuremath{\rightarrow}\ensuremath{\phi}\ensuremath{\mu}\ensuremath{\nu}$, and the other ${D}_{s}^{(*)}$ meson was identified using the decay ${D}_{s}\ensuremath{\rightarrow}\ensuremath{\phi}\ensuremath{\pi}$ where no attempt was made to distinguish ${D}_{s}$ and ${D}_{s}^{*}$ states. For the branching fraction $\mathrm{Br}({B}_{s}^{0}\ensuremath{\rightarrow}{D}_{s}^{(*)}{D}_{s}^{(*)})$ we obtain a 90% C.L. range $[0.002,0.080]$ and central value ${0.039}_{\ensuremath{-}0.017}^{+0.019}(\mathrm{stat}{)}_{\ensuremath{-}0.015}^{+0.016}(\mathrm{syst})$. This was subsequently used to make the most precise estimate of the width difference $\ensuremath{\Delta}{\ensuremath{\Gamma}}_{s}^{CP}$ in the ${B}_{s}^{0}\ensuremath{-}{\overline{B}}_{s}^{0}$ system: $\ensuremath{\Delta}{\ensuremath{\Gamma}}_{s}^{CP}/{\ensuremath{\Gamma}}_{s}={0.079}_{\ensuremath{-}0.035}^{+0.038}(\mathrm{stat}{)}_{\ensuremath{-}0.030}^{+0.031}(\mathrm{syst})$.