Abstract The decay B 0 → DK *0 and the charge conjugate mode are studied using 1.0 fb−1 of pp collision data collected by the LHCb experiment at $ \sqrt{s}=7 $ TeV in 2011. The CP asymmetry between the B 0 → DK *0 and the $ {{\overline{B}}^0}\to D{{\overline{K}}^{*0 }} $ decay rates, with the neutral D meson in the CP-even final state K + K −, is found to be $ \mathcal{A}_d^{KK }=-0.45\pm 0.23\pm 0.02, $ where the first uncertainty is statistical and the second is systematic. In addition, favoured B 0 → DK *0 decays are reconstructed with the D meson in the non-CP eigenstate K +π−. The ratio of the B-flavour averaged decay rates in D decays to CP and non-CP eigenstates is measured to be $ \mathcal{R}_d^{KK }=1.36_{-0.32}^{+0.37}\pm 0.07, $ where the ratio of the branching fractions of D 0 → K −π+ to D 0 → K + K − decays is included as multiplicative factor. The CP asymmetries measured with two control channels, the favoured B 0 → DK *0 decay with D → K +π− and the $ \overline{B}_s^0\to D{K^{*0 }} $ decay with D→K + K −, arealsoreported.