A model-dependent amplitude analysis of the decay B 0 → D(K S 0 π + π −)K ∗ 0 is performed using proton-proton collision data corresponding to an integrated luminosity of 3.0 fb−1, recorded at s√=7s=7 and 8 TeV by the LHCb experiment. The CP violation observables x ± and y ±, sensitive to the CKM angle γ, are measured to be x−=−0.15±0.14±0.03±0.01,y−=0.25±0.15±0.06±0.01,x+=0.05±0.24±0.04±0.01,y+=−0.65+0.24−0.23±0.08±0.01, x−=−0.15±0.14±0.03±0.01,y−=0.25±0.15±0.06±0.01,x+=0.05±0.24±0.04±0.01,y+=−0.65−0.23+0.24±0.08±0.01, where the first uncertainties are statistical, the second systematic and the third arise from the uncertainty on the D → K S 0 π + π − amplitude model. These are the most precise measurements of these observables. They correspond to γ = (80 − 22 + 21 )° and rB0=0.39±0.13rB0=0.39±0.13, where rB0rB0 is the magnitude of the ratio of the suppressed and favoured B 0 → DK + π − decay amplitudes, in a Kπ mass region of ±50 MeV around the K *(892)0 mass and for an absolute value of the cosine of the K *0 decay angle larger than 0.4.