A binned Dalitz plot analysis of the decays B 0 → DK ∗0, with D → K S 0 π + π − and D → K S 0 K + K −, is performed to measure the observables x ± and y ±, which are related to the CKM angle γ and the hadronic parameters of the decays. The D decay strong phase variation over the Dalitz plot is taken from measurements performed at the CLEO-c experiment, making the analysis independent of the D decay model. With a sample of proton-proton collision data, corresponding to an integrated luminosity of 3.0 fb−1, collected by the LHCb experiment, the values of the CP violation parameters are found to be x + = 0.05 ± 0.35 ± 0.02, x − = −0.31 ± 0.20 ± 0.04, y + = −0.81 ± 0.28 ± 0.06 and y − = 0.31 ± 0.21 ± 0.05, where the first uncertainties are statistical and the second systematic. These observables correspond to values γ = (71 ± 20)°, $$ {r_B}_{{}^0}=0.56\pm 0.17 $$ and $$ {\delta_B}_{{}^0}=\left(20{4}_{-20}^{+21}\right){}^{\circ} $$ . The parameters $$ {r_B}_{{}^0} $$ and $$ {\delta_B}_{{}^0} $$ are the magnitude ratio and strong phase difference between the suppressed and favoured B 0 decay amplitudes, and have been measured in a region of ±50 MeV/c 2 around the K ∗(892)0 mass and with the magnitude of the cosine of the K ∗(892)0 helicity angle larger than 0.4.