We investigate the effect of the surface treatment on the electrical response of a nematic liquid crystal cell. Our analysis shows that the relaxation time of the current is strongly dependent on the electrical properties of the surface layer. The theoretical analysis is performed by describing the liquid crystal and the surface treatment by means of the dielectric constants and the electrical conductivities. The predictions of the model are compared with the measurements performed on a nematic cell submitted to an external voltage step-like or linear in time. The good agreement between the prediction and the experimental data allows using these kind of measurements to characterize, from the electrical point of view, a nematic cell of the type considered in our analysis.