The effect of indium doping on the point defect formation in ZnO nanostructures is studied by scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) techniques. While the incorporation of a donor dopant like indium should increase the n-type conductivity of ZnO nanostructures, it has been found that formation of V(Zn) native acceptors in heavily doped ZnO nanostructures produces self-compensation effect, creating acceptor states in their band gap. Presence of both donor and acceptor states in heavily indium doped ZnO nanostructures are probed and identified. The mechanism of formation of such donor and acceptor states is discussed.