We investigate the dopant concentration and majority carrier mobility in epitaxial CuInSe2 thin films for different copper-to-indium ratios and selenium excess during growth. We find that all copper-poor samples are n-type, and that hopping conduction in a shallow donor state plays a significant role for carrier transport. Annealing in sodium ambient enhances gallium in-diffusion from the substrate wafer and changes the net doping of the previously n-type samples to p-type. We suggest that sodium incorporation from the glass might be responsible for the observed p-type doping in polycrystalline Cu-poor CuInSe2 solar cell absorbers.