We fabricate photodetectors based on solution-processed single CH3NH3PbBr3 microcrystals (MCs) and map the two-photon absorption (TPA) excited photocurrent (PC) with spatial resolution of 1 μm. We find that the charge carrier transport length in the MCs depends on the applied electric field, and increases from 5.7 μm for 0.02 V bias (dominated by carrier diffusion) to 23.2 μm for 2 V bias (dominated by carrier drift). Furthermore, PC shows strong spatial variations. Combining the PC mapping results with time-resolved photoluminescence microscopy, we demonstrate that the spatial distribution of PC mainly originates from the inhomogeneous distribution of trap-states across perovskite MCs. This suggests that there is still large margin for improvement of perovskite single crystal devices by better controlling of the traps.