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The comprehension of conduction mechanisms in single-walled carbon nanotubes is a crucial task for developing efficient nanodevices. Appealing hybrid architectures could exploit charge transport perpendicular to the main nanotube axis in order to minimize carrier path and phonon scattering effects. Such transverse transport is investigated in metallic and semiconducting nanotubes by means of conductive atomic force microscopy. The transverse current response is interpreted in the framework of a tunneling transport model, and reveals that conduction across metallic nanotubes is either tunneling- or bandlike, depending on the force applied by the tip, while charge carriers always tunnel through the semiconducting nanotubes.