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Hybrid organic-inorganic methylammonium (MA) lead-halide perovskite MAPbI3 has shown record-breaking photovoltaic conversion efficiency and demonstrated great potential in solar cell applications. Its unusual long carrier lifetime has drawn much research interest, yet its origin remains a debated subject. Whether or not the tetragonal phase of this material is polar is key to resolve the ongoing debates. In this talk, we present clarifying evidence to show the absence of spatial inversion symmetry in single-crystalline MAPbI3 bulk over a wide temperature range starting from 300 K down to 80K, using rotational anisotropy (RA) second harmonic generation (SHG) spectroscopy. We will further discuss the tetragonal to orthorhombic structural phase transition, by analyzing the temperature-dependence of SHG susceptibility tensors. Finally, we will discuss how this non-centrosymmetric phase response to ultrafast optical excitations, from the time-resolved RA SHG measurement results.