The crystal structure of the manganite Nd₀.₅Sr₀.₅MnO₃ is studied at temperatures T=300 and 77.3 K by means of an x-ray diffractometer. It is shown that the transition from the ferromagnetic metallic state to the antiferromagnetic insulating charge-ordered state is accompanied by a lowering of the symmetry of the structure from orthorhombic to monoclinic. The space-group symmetry of the orthorhombic and monoclinic phases is identified as Imma and P21 / m, respectively. Twinning of the crystal and the formation of a twin domain structure with coherent boundaries in the (00l) crystallographic planes are found.