A gas turbine engine includes a case assembly and a stator segment. The case assembly defines a first slot having a first surface and a second surface. The stator segment includes a shroud body axially extends between a first body end and a second body end. A first flange extends into the first slot. The first flange has a first flange first side, a first flange second side, a first flange first surface and a first flange second surface each circumferentially extending between the first flange first side and the first flange second side. A first portion of the first flange first surface engages the first surface. A second portion of the first flange first surface. A third portion of the first flange first surface is spaced apart from the first surface.