The first measurement of decay-time-dependent CP asymmetries in the decay $B_s^0rightarrow J/psi K_{rm S}^0$ and an updated measurement of the ratio of branching fractions $mathcal{B}(B_s^0rightarrow J/psi K_{rm S}^0)/mathcal{B}(B_d^0rightarrow J/psi K_{rm S}^0)$} 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 $A_{DeltaGamma}(B_s^0rightarrow J/psi K_{rm S}^0) = 0.49_{-0.65}^{+0.77}(stat) pm 0.06(syst)$, $C_{rm dir}(B_s^0rightarrow J/psi K_{rm S}^0) = -0.28 pm 0.41(stat) pm 0.08(syst)$ and $S_{rm mix}(B_s^0rightarrow J/psi K_{rm S}^0) = -0.08 pm 0.40(stat) pm 0.08(syst)$. The ratio $mathcal{B}(B_s^0rightarrow J/psi K_{rm S}^0)/mathcal{B}(B_d^0rightarrow J/psi K_{rm S}^0)$ is measured to be $0.0431 pm 0.0017(stat) pm 0.0012(syst) pm 0.0025(f_s/f_d)$, where the last uncertainty is due to the knowledge of the $B_s^0$ and $B_d^0$ production fractions.
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