The synthesis of metal-organic frameworks (MOFs) as thin films allows their integration into different electronic devices. Particularly, their application in metal-insulating-semiconductor (MIS) capacitors provides a comprehensive study of the electrical transport mechanism and, therefore, of the effect of border traps. A low concentration of border traps guarantees a good performance of MIS capacitors. This paper is focused on the investigation of the charge components within the MOF and near the MOF/substrate interface in ultrathin Cu3(BTC)2 films grown directly on silicon wafers by an innovative spray-coating method. The layer thickness was easily handled by varying the number of spray cycles in the deposition process. The crystal structure and morphology of the films were characterized via X-ray diffraction and Raman spectroscopy. Afterwards, the film thickness was determined via confocal microscopy. The electrical characterization was performed via capacitance-voltage (C-V) measurements in forward and reverse direction at room temperature and at different frequencies. Our results provide evidence of the existence of positive fixed charges in the Cu3(BTC)2 dielectric layer as well as of the presence of border traps which causes hysteresis in the C-V response.