A turbine section for a gas turbine engine comprising: a turbine support case extending circumferentially around an axis, the turbine support case having a shroud supporting structure; a circumferential array of turbine blades disposed within the turbine support case for rotation about the axis; and a circumferentially segmented turbine shroud mounted inside the turbine support case about the circumferential array of turbine blades, the circumferentially segmented turbine shroud including a plurality of shroud segments disposed circumferentially one adjacent to another, each of the shroud segments comprising a shroud body including: a platform having a radially inner surface facing towards the axis and a radially outer surface facing away from the axis; forward and aft hooks (40,42) extending from the radially outer surface of the platform for engagement with the shroud support structure on the turbine support case; a pin receiving hole extending axially in a radially extending leg portion (40a, 42a) of one of the forward and aft hooks (40,42) of the shroud body; characterised by an anti-rotation pin engaged in the pin receiving hole, the anti-rotation pin projecting outwardly from the pin receiving hole for engagement with a corresponding anti-rotation abutment on the shroud support structure, wherein the anti-rotation pin has a shank portion pressed fit in the pin receiving hole and an enlarged head portion loosely received in a localisation slot defined in a distal end of a rail portion (24a, 24b) of the shroud supporting structure. a turbine support case extending circumferentially around an axis, the turbine support case having a shroud supporting structure; a circumferential array of turbine blades disposed within the turbine support case for rotation about the axis; and a circumferentially segmented turbine shroud mounted inside the turbine support case about the circumferential array of turbine blades, the circumferentially segmented turbine shroud including a plurality of shroud segments disposed circumferentially one adjacent to another, each of the shroud segments comprising a shroud body including: a platform having a radially inner surface facing towards the axis and a radially outer surface facing away from the axis; forward and aft hooks (40,42) extending from the radially outer surface of the platform for engagement with the shroud support structure on the turbine support case; a pin receiving hole extending axially in a radially extending leg portion (40a, 42a) of one of the forward and aft hooks (40,42) of the shroud body; characterised by an anti-rotation pin engaged in the pin receiving hole, the anti-rotation pin projecting outwardly from the pin receiving hole for engagement with a corresponding anti-rotation abutment on the shroud support structure, wherein the anti-rotation pin has a shank portion pressed fit in the pin receiving hole and an enlarged head portion loosely received in a localisation slot defined in a distal end of a rail portion (24a, 24b) of the shroud supporting structure. a platform having a radially inner surface facing towards the axis and a radially outer surface facing away from the axis; forward and aft hooks (40,42) extending from the radially outer surface of the platform for engagement with the shroud support structure on the turbine support case; a pin receiving hole extending axially in a radially extending leg portion (40a, 42a) of one of the forward and aft hooks (40,42) of the shroud body; characterised by an anti-rotation pin engaged in the pin receiving hole, the anti-rotation pin projecting outwardly from the pin receiving hole for engagement with a corresponding anti-rotation abutment on the shroud support structure, wherein the anti-rotation pin has a shank portion pressed fit in the pin receiving hole and an enlarged head portion loosely received in a localisation slot defined in a distal end of a rail portion (24a, 24b) of the shroud supporting structure.