Thin films of nanostructures alter the electrical properties of mineral surfaces and thereby affect reactions with charged species such as metal ions and biological cells. In this study, electric-force microscopy is used to probe the electrical properties of a heterogeneous layout of manganese oxide nanostructures grown as a film on a MnCO3 substrate. The role of water sorption is examined by carrying out experiments for increasing relative humidity (RH). Electric-force images collected with a negative dc tip bias show that the apparent heights of the nanostructures decrease from +3.4 nm at 16% RH to +0.7 nm at 33% RH to -5.6 nm at 74% RH, although the topographic height is 2.3 nm regardless of RH. The apparent heights for a positive dc bias also decrease with increasing RH from -3.5 nm at 16% RH to -8.9 nm at 74%. The explanation for these trends is that the dominant electric-force transitions with increasing RH from an electrostatic force attributable to surface potential to a polarization force arising from hydrated, mobile surface ions including Mn2+ and CO32-. The positive-to-negative trend in apparent heights implies that either the density or the intrinsic mobility (or both) of mobile ions over the substrate exceeds that over the nanostructures, implying increased water sorption over the former compared to the latter. Ridges around the perimeter of the nanostructures also develop above 40% RH for images collected using a negative dc tip bias. A tip-induced gradient of net positive charge near the nanostructure edges, which implies the nonequivalence of cations and anions there, explain this observation. The findings of this study show that thin films of nanostructures on mineral surfaces have complex but measurable RH-dependent electrical properties.