The first measurement of decay-time-dependent CP asymmetries in the decay B s 0 → J/ψK S 0 and an updated measurement of the ratio of branching fractions $$ \mathrm{\mathcal{B}}\left({B}_{\mathrm{s}}^0\to J/\psi {K}_{\mathrm{S}}^0\right)/\mathrm{\mathcal{B}}\left({B}^0\to J/\psi {K}_{\mathrm{S}}^0\right) $$ are presented. The results are obtained using data corresponding to an integrated luminosity of 3.0 fb−1 of proton-proton collisions recorded with the LHCb detector at centre-of-mass energies of 7 and 8 TeV. The results on the CP asymmetries are $$ \begin{array}{l}{\mathcal{A}}_{\Delta \Gamma}\left({B}_s^0\to J/\psi {K}_{\mathrm{S}}^0\right)=0.49{\pm}_{0.65}^{0.77}\left(\mathrm{stat}\right)\pm 0.06\left(\mathrm{syst}\right),\hfill \\ {}{C}_{\mathrm{dir}}\left({B}_s^0\to J/\psi {K}_{\mathrm{S}}^0\right)=-0.28\pm 0.41\left(\mathrm{stat}\right)\pm 0.08\left(\mathrm{syst}\right),\hfill \\ {}{S}_{\mathrm{mix}}\left({B}_s^0\to J/\psi {K}_{\mathrm{S}}^0\right)=-0.08\pm 0.40\left(\mathrm{stat}\right)\pm 0.08\left(\mathrm{syst}\right).\hfill \end{array} $$ The ratio $$ \mathrm{\mathcal{B}}\left({B}_{\mathrm{s}}^0\to J/\psi {K}_{\mathrm{S}}^0\right)/\mathrm{\mathcal{B}}\left({B}^0\to J/\psi {K}_{\mathrm{S}}^0\right) $$ is measured to be $$ 0.0431\pm 0.0017\left(\mathrm{stat}\right)\pm 0.0012\left(\mathrm{syst}\right)\pm 0.0025\left({f}_s/{f}_d\right), $$ where the last uncertainty is due to the knowledge of the B s 0 and B 0 production fractions.