We have performed a piezoresponse force microscopy (PFM) study on methylammonium lead iodide (MAPbI(3)) thin films in normal (non-resonance, non-band-excitation) contact mode. In contrast to the ferroelectric Pb0.76Ca0.24TiO3 (PCT) control sample, a typical ferroelectric response was not observed. However, a nonlinear electric field dependence of the local PFM amplitude was found in MAPbI(3), similar to PCT. An analysis combining results on structure, dielectric dispersion, and weak ferroelectricity demonstrates that MAPbI3 is actually a re-entrant relaxor ferroelectric which, upon cooling, enters into a relaxor phase below its ferroelectric phase transition at similar to 327 K, due to the balance between the long range ferroelectric order and structural methylammonium group orientational disorder. The ferroelectricity at room temperature is compromised due to the re-entrant relaxor behavior, causing the poor polarization retention or weak ferroelectricity. Our findings essentially conciliate the conflicting experimental results on MAPbI(3)'s ferroelectricity and are beneficial both for basic understanding as well as for device applications. (C) 2016 Elsevier B.V. All rights reserved