The ease of processing hybrid organic-inorganic perovskite (HOIPs) films, belonging to a material class with composition ABX3 , from solution and at mild temperatures promises their use in deformable technologies, including flexible photovoltaic devices, sensors, and displays. To successfully apply these materials in deformable devices, knowledge of their mechanical response to dynamic strain is necessary. The authors elucidate the time- and rate-dependent mechanical properties of HOIPs and an inorganic perovskite (IP) single crystal by measuring nanoindentation creep and stress relaxation. The observation of pop-in events and slip bands on the surface of the indented crystals demonstrate dislocation-mediated plastic deformation. The magnitudes of creep and relaxation of both HOIPs and IPs are similar, negating prior hypothesis that the presence of organic A-site cations alters the mechanical response of these materials. Moreover, these samples exhibit a pronounced increase in creep, and stress relaxation as a function of indentation rate whose magnitudes reflect differences in the rates of nucleation and propagation of dislocations within the crystal structures of HOIPs and IP. This contribution provides understanding that is critical for designing perovskite devices capable of withstanding mechanical deformations.