Vapor-grown carbon nanofibers (VGCNF) functionalized with amine-containing pendants, viz.H2N-VGCNF, reacted with 2,2-bis(phthalic anhydride)-1,1,1,3,3,3-hexafluoroisopropane, which was the dianhydride monomer used in in-situ polymerization with 1,3-bis(3-aminophenoxy)benzene to afford a series of CP2-polyimide nanocomposite films (FCNFCP2), containing 0.18-9.19 wt % of H2N-VGCNF (corresponding to 0.10-5.0 wt % of pristine VGCNF), via conventional poly(amic acid) precursor method. For comparison, another series of in situ nanocomposites containing pristine VGCNF (0.10-5.0 wt %) was also prepared similarly. While H2N-VGCNFs enabled direct formation of CP2 grafts on the nanofibers, pristine VGCNFs would result in a relatively weak interface between nanofibers and the CP2 matrix. Conducting-tip atomic force microscopy (C-AFM) showed that the electrical transport was solely through the nanofiber networks in the PCNF-CP2. In general, low-frequency ac impedance measurements followed well the percolation bond model with low percolation threshold; 0.24 and 0.68 vol % for PCNF-CP2 and FCNF-CP2, respectively. However, the design of interface is determined to be crucial for controlling the electrical behavior in four substantial ways: (i) magnitude of limiting conductivity, (ii) linearity of I-V response, (iii) magnitude and direction of temperature-dependent resistivity, and (iv) reproducibility of the absolute value of resistivity with thermal cycling. These observations are consistent with a direct CNF-CNF contact limiting transport in the PCNF-CP2 system, where the CP2 grafts on FCNF form a dielectric layer between individual CNFs, limiting transport within the FCNF-CP2 system. Furthermore, the CP2 grafts on the FCNF surface reduce local polymer dewetting at the nanofiber surfaces when the temperatures exceed the CP2 glass transition, and stabilize the structure of the percolation network and associated conductivity. The general behavior of these interfacial extremes (pristine and fully functionalized CNFs) set important bounds on the design of interface modification for CNFs when the intended use is for electrical performance at elevated temperatures or under extreme current loads. The influence of processing conditions resulting in the spread of measured conductivity by several orders of magnitude for films containing the same type and same amount of CNFs is also reported.