Measurements of CP observables in B± → DK*± decays are presented, where D denotes a superposition of D0 and D¯¯¯¯0D¯0 meson states. Decays of the D meson to K−π+, K−K+, π−π+, K−π+π−π+ and π−π+π−π+ are used and the K*± meson is reconstructed in the KS0π± final state. This analysis uses a data sample of pp collisions collected with the LHCb experiment, corresponding to integrated luminosities of 1 fb−1, 2 fb−1 and 1.8 fb−1 at centre-of-mass energies s√=7s=7 TeV, 8 TeV and 13 TeV, respectively. The sensitivity of the results to the CKM angle γ is discussed.