  The crystal structure of the candidate topological superconductor
Cu$_x$Bi$_2$Se$_3$ was studied by single-crystal neutron diffraction using
samples obtained by inserting the Cu dopant electrochemically. Neither
structural refinements nor calculated scattering-density maps find a
significant occupation of Cu at the intercalation site between the quintuple
layers of Bi$_2$Se$_3$. Following Bragg reflection intensities as function of
temperature, there is no signature of a structural phase transition between 295
and 2 K. However, the analysis of large sets of Bragg reflections indicates a
small structural distortion breaking the rotational axis due to small
displacements of the Bi ions.
