Metal halide perovskites such as methylammonium lead iodide (CH3NH3PbI3) are generating great excitement due to their outstanding optoelectronic properties, which lend them to application in high-efficiency solar cells and light-emission devices. However, there is currently debate over what drives the second-order electron-hole recombination in these materials. Here, we propose that the bandgap in CH3NH3PbI3 has a direct-indirect character. Time-resolved photo-conductance measurements show that generation of free mobile charges is maximized for excitation energies just above the indirect bandgap. Furthermore, we find that second-order electron-hole recombination of photo-excited charges is retarded at lower temperature. These observations are consistent with a slow phonon-assisted recombination pathway via the indirect bandgap. Interestingly, in the low-temperature orthorhombic phase, fast quenching of mobile charges occurs independent of the temperature and photon excitation energy. Our work provides a new framework to understand the optoelectronic properties of metal halide perovskites and analyse spectroscopic data.