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The crystal structure of the candidate topological superconductorCu$_x$Bi$_2$Se$_3$ was studied by single-crystal neutron diffraction usingsamples obtained by inserting the Cu dopant electrochemically. Neitherstructural refinements nor calculated scattering-density maps find asignificant occupation of Cu at the intercalation site between the quintuplelayers of Bi$_2$Se$_3$. Following Bragg reflection intensities as function oftemperature, there is no signature of a structural phase transition between 295and 2 K. However, the analysis of large sets of Bragg reflections indicates asmall structural distortion breaking the rotational axis due to smalldisplacements of the Bi ions.

Crystal structure and distortion of superconducting Cu$_x$Bi$_2$Se$_{3}$