The role of the surface layers in La2/3Ca1/3MnO3 magnetic oxide epitaxial thin films is analyzed. We show that the topmost layers do play a very relevant role on the transport properties acting as an insulating barrier. Atomic force microscopy (AFM) measurements in the current sensing mode exhibit typical features of tunneling conduction. The analysis of the I-V curves by using the Simmons model give values of barrier thickness in good agreement with nonmagnetic layer thickness estimates from magnetic measurements. Ex situ annealing in air at high temperature clearly improve the magnetotransport properties of the films reducing the surface insulating barrier.