A search for the decay $B_{s}^0 rightarrow overline{K}{}^{*0}mu^+mu^-$ is presented using data sets corresponding to 1.0, 2.0 and 1.6 $text{fb}^{-1}$ of integrated luminosity collected during $pp$ collisions with the LHCb experiment at centre-of-mass energies of 7, 8 and 13 TeV, respectively. An excess is found over the background-only hypothesis with a significance of 3.4 standard deviations. The branching fraction of the $B_{s}^0 rightarrow overline{K}{}^{*0}mu^+mu^-$ decay is determined to be $mathcal{B}(B_{s}^0 rightarrow overline{K}{}^{*0}mu^+mu^-) = [2.9 pm 1.0~(text{stat}) pm 0.2~(text{syst}) pm 0.3~(text{norm})] times 10^{-8}$, where the first and second uncertainties are statistical and systematic, respectively. The third uncertainty is due to limited knowledge of external parameters used to normalise the branching fraction measurement.
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