We present an in-depth electrical characterization of contact resistance in carbon nanostructure via interconnects. Test structures designed and fabricated for via applications contain vertically aligned arrays of carbon nanofibers (CNFs) grown on a thin titanium film on silicon substrate and embedded in silicon dioxide. Current-voltage measurements are performed on single CNFs using atomic force microscope current-sensing technique. By analyzing the dependence of measured resistance on CNF diameter, we extract the CNF resistivity and the metal-CNF contact resistance.