An assembly of packed and oriented rodlike particles exhibit anisotropic physical properties. We investigate in the present work the anisotropic conductivity of films made of intrinsically conducting rods. These films are obtained from more or less ordered carbon nanotube liquid crystals. Their orientational order parameter is measured by polarized Raman spectroscopy. A relationship between the anisotropy of surface conductivity and orientational order parameter is determined. The experimental results are accounted for by a model that takes into account the number of intertube contacts and density of conductive pathways in different directions, as introduced by J. Fischer et al. for magnetically aligned nanotubes. We find that a good agreement, without any fitting parameter, of the proposed model and experiments is obtained when we consider a two-dimensional (2D) Gaussian distribution of the nanotube orientation. The conductivities parallel and perpendicular to the nematic director differ by almost an order of magnitude. This anisotropy is much greater than that of conventional dielectric liquid crystals, where the behavior is governed by the mobility anisotropy of ionic current carriers. The present results do not depend on the intrinsic properties of the nanotubes and are expected to be relevant for other assemblies of conducting rodlike particles, such as metallic or semi-conducting nanowires and ribbons.