Defect tolerance is an extremely important aspect in nano-scale electronics as the bottom-up self-assembly fabrication process results in a significantly higher defect density compared to conventional lithography-based process. Defect tolerance techniques are therefore essential to obtain an acceptable manufacturing yield. In this paper we investigate defect tolerance properties of a two-dimensional (2D) nano-scale crossbar, which is the basic block of various nano architectures which have been recently proposed. Various nano-wire and switch faults are studied and their impact on the routability of a crossbar are investigated. In the presence of defects, it is still possible to utilize a defective crossbar at reduced functionality, i.e. as a smaller defect-free crossbar. Simulation results for different sizes and defect densities are presented. This proposed approach can be utilized by architecture designers to determine the expected size of functional (defect-free) crossbar based on defect density information obtained from the fabrication process.