We present time-resolved Kerr rotation (TRKR) spectra in thin films of CH3NH3PbI3 (MAPI) hybrid perovskite using a unique picosecond microscopy technique at 4 K having a spatial resolution of 2 μm and temporal resolution of 1 ps, subjected to both an in-plane applied magnetic field up to 700 mT and an electric field up to 104 V/cm. We demonstrate that the obtained TRKR dynamics and spectra are substantially inhomogeneous across the MAPI films with prominent resonances at the exciton energy and interband transition of this compound. From the obtained quantum beating response as a function of magnetic field in the Voigt configuration, we also extract the inhomogeneity of the electron and hole Lande g-values and spin coherence time, T2*. We also report the TRKR dependence on both the applied magnetic field and electric field. From the change in the quantum beating dynamics, we found that T2* substantially decreases upon the application of an electric field. At the same time, from the induced spatial TRKR changes, we show that the electric field induced effects are caused by ion migration in the MAPI films.