We present a non-local thermodynamic equilibrium retrieval scheme for atmospheric composition and its application to Mars CO2 infrared limb emissions as measured by the OMEGA instrument on board Mars Express (MEx). These emissions are caused by CO2 fluorescence of solar radiation, and thus the retrieval scheme accounts for non-LTE processes. We analyzed the dayside limb observations from a selection of three OMEGA orbits or data qubes. Before the retrieval was applied, we performed a radiometric calibration, cleaned the spectra (including clustering techniques) and generated radiance vertical profiles for each dataset. We also present information on the inversion set up, results on the retrieved CO2 density profiles, as well as the temperature profiles derived from the CO2 densities by assuming hydrostatic equilibrium. An extensive sensitivity study of the retrieval scheme was carried out, including its application to the OMEGA spectra taken at different MEx orbital configurations, to conclude on its performance and to offer recommendations for its systematic use with MEx datasets. The uncertainty due to the instrumental Gain calibration and that caused by the retrieval noise error itself are of large importance for the inversion, but a comparable component of the total error comes from the uncertainties of the temperature provided by the GCM. We demonstrated that, between 120 and 160 km, CO2 profiles can be derived with a precision around 30% and a vertical resolution of about 15 km.