A bstract Measurements of CP observables in B ± → DK *± decays are presented, where D denotes a superposition of D 0 and $$ {\overline{D}}^0 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mover> <mml:mi>D</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mn>0</mml:mn> </mml:msup> </mml:math> 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 K S 0 π ± 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 $$ \sqrt{s}=7 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mi>s</mml:mi> </mml:msqrt> <mml:mo>=</mml:mo> <mml:mn>7</mml:mn> </mml:math> TeV, 8 TeV and 13 TeV, respectively. The sensitivity of the results to the CKM angle γ is discussed.