The first measurement of decay-time-dependent CP asymmetries in the decay Bs0 J/KS0and an updated measurement of the ratio of branching fractions Bs0J/KS0/B0J/KS0$$ \mathrm{\mathcal{B}}\left({B}_{\mathrm{s}}^0\to J/\psi {K}_{\mathrm{S}}^0\right)/\mathrm{\mathcal{B}}\left({B}^0\to J/\psi {K}_{\mathrm{S}}^0\right) $$are presented. The results are obtained using data corresponding to an integrated luminosity of 3.0 fb1 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 areABs0J/KS0=0.49±0.650.77stat±0.06syst,CdirBs0J/KS0=0.28±0.41stat±0.08syst,SmixBs0J/KS0=0.08±0.40stat±0.08syst.$$ \begin{array}{l}{\mathcal{A}}_{\Delta \Gamma}\left({B}_s^0\to J/\psi {K}_{\mathrm{S}}^0\right)=0.49{\pm}_{0.65}^{0.77}\left(\mathrm{stat}\right)\pm 0.06\left(\mathrm{syst}\right),\hfill \\ {}{C}_{\mathrm{dir}}\left({B}_s^0\to J/\psi {K}_{\mathrm{S}}^0\right)=-0.28\pm 0.41\left(\mathrm{stat}\right)\pm 0.08\left(\mathrm{syst}\right),\hfill \\ {}{S}_{\mathrm{mix}}\left({B}_s^0\to J/\psi {K}_{\mathrm{S}}^0\right)=-0.08\pm 0.40\left(\mathrm{stat}\right)\pm 0.08\left(\mathrm{syst}\right).\hfill \end{array} $$
