In order to better understand the structure and dynamics of methylammonium lead halide perovskites, we performed NMR, NQR, and DFT studies of CHNHPbI in the tetragonal and cubic phase. Our results indicate that the space group of the tetragonal phase is the nonpolar I4/mcm. The highly dynamic methylammonium moiety shows no indication of the occurrence of additional orientations of the C-N bond close to the c-axis at temperatures approaching the cubic phase. Crystal quality effects are shown to influence the N NMR andI NQR spectra, and the effects of high-temperature annealing on defects can be observed. A strong increase in T relaxation time of the Pb NMR signal on cooling is found, and is an indication of slow motions in the PbI octahedra at room temperature. These results aid in the understanding of the structure of methylammonium lead halides and enable further studies of defects in these materials.