Powder neutron diffraction and Hi-Q neutron diffraction data have been recorded and analysed in order to obtain the local and long range order of Cu in Cu-doped CeO₂ with three doping levels of Cu. Rietveld method and MCGR techniques of data analysis for the two types of data reveal that the Cu ion is in the 2+ oxidation state and has a vacancy in its first coordination shell. These deductions from the data analysis fit well with the mechanism of catalysis we propose.