A search for the decay $B^0_srightarrow J/psi K^{*0}$ with $K^{*0} rightarrow K^-pi^+$ is performed with 0.37 fb$^{-1}$ of $pp$ collisions at $sqrt{s}$ = 7 TeV collected by the LHCb experiment, finding a $Bs to Jpsi K^-pi^+$ peak of $114 pm 11$ signal events. The $K^-pi^+$ mass spectrum of the candidates in the $B^0_s$ peak is dominated by the $K^{*0}$ contribution. Subtracting the non-resonant $K^-pi^+$ component, the branching fraction of BsJpsiKst is $(4.4_{-0.4}^{+0.5} pm 0.8) times 10^{-5}$, where the first uncertainty is statistical and the second systematic. A fit to the angular distribution of the decay products yields the Kst polarization fractions $f_L = 0.50 pm 0.08 pm 0.02$ and $f_{||} = 0.19^{+0.10}_{-0.08} pm 0.02$.
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