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Reduction in contact resistance is one of the foremost challenges for carbon nanotube/graphene nanodevices. In this study, we present a novel fabrication process for low-temperature, Ohmic contact between open-ended multiwalled carbon nanotubes (MWCNTs) and metal interconnects using graphitic carbon deposited via electron beam-induced deposition (EBID). The electrical and structural properties of the contact interface are characterized for making connection to the single (outermost) shell only, as well as to multiple conducting shells of MWCNTs. In addition to establishing the scaling relationship between the carbon contact length and the resulting contact resistance, the magnitude of the contact resistance has been quantified with and without post-deposition thermal annealing. The results indicate that the contact is Ohmic in nature, and ranges from 26.5 kΩ for the connection made to the outermost shell of an MWCNT down to just 116 Ω for the multiple-shell connection performed via a process suggested through the EBID process simulations. These results provide a significant advance in application of MWCNTs to future interconnect technologies.