  The first measurement of ${C\!P}$ asymmetries in the decay ${B_s^0\to J/\psi
\overline{K}^{*}(892)^{0}}$ and an updated measurement of its branching
fraction and polarisation fractions 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 $8\,\mathrm{TeV}$. Together with constraints from ${B^0\to
J/\psi \rho^0}$, the results are used to constrain additional contributions due
to penguin diagrams in the ${C\!P}$-violating phase ${{\phi}_{s}}$, measured
through ${B_s^0}$ decays to charmonium.
