Current voltage and Kelvin Probe Force Microscopy (KPFM) measurements were performed on single ZnO nanowires. Measurements are shown to be strongly correlated with the contact behavior, either ohmic or Schottky. The ZnO nanowires were obtained by metallo-organic chemical vapor deposition (MOCVD) and contacted using electronic-beam lithography. Depending on the contact geometry, good quality ohmic contacts (linear I V behavior) or non-linear (diode like) Schottky contacts were obtained. Current voltage and KPFM measurements on both types of contacted ZnO nanowires were performed in order to investigate their behavior. A clear correlation could be established between the I V curve, the electrical potential profile along the device and the nanowire geometry. Some arguments supporting this behavior are given based on a depleted region extension. This work will help to better understand the electrical behavior of ohmic contacts on single ZnO nanowires, for future applications in nanoscale field effect-transistors and nano-photodetectors.