The effect of a localized surface viscosity on the relaxation of a pre-existing deformation in a nematic liquid crystal cell is perturbatively analyzed in the presence of an external field. When the surface viscosity of the system is small enough to use perturbation developments, approximated solutions can be obtained describing the space-time profile of the director angle. It is shown that if the surface viscosity increases, the relaxation becomes slower when compared to the case corresponding to the absence of viscosity. The temporal behavior of the optical path difference is analytically established by incorporating the contribution of the surface viscosity.