Perovskite solar cells based on methylammonium lead iodide (CH3NH3PbI3) and related materials have emerged as an exciting development for next generation photovoltaic technologies. Solar cells based on them have achieved impressive energy conversion efficiencies, but their stability is still limited. Understanding degradation mechanisms in such materials is key to developing strategies to increase their lifetime. The present work reports on the nanoscale characterization of perovskite photovoltaic films with respect to their stability and degradation mechanisms. We investigated the local conductance variations and current-voltage characteristics of perovskite films at the nanoscale using conducting atomic force microscopy (CAFM). CAFM measurements revealed that the current is larger at grain boundaries, and that the average grain size, determined by the post-deposition heat treatment, affects the film`s conductance. Further studies will examine the effect of sunlight exposure on the nano-scale conductance of perovskite thin films towards better understanding of photo-induced degradation mechanisms.