The aim of this work is to develop a high spatial resolution, high sensitivity, compact PET detector for small animal PET/MR imaging. The key design features are the use of trapezoidal slat crystals (TSC), the use of silicon photomultiplier (SiPM) arrays, and the use of a 3D statistics based positioning (SBP) algorithm. Through simulation, the performance of a detector module consisting of 8 trapezoidal 0.92 mm (0.63 mm) by 47.52 mm by 12 mm crystals readout by a 2x12 SiPM array was evaluated. A PET detector ring with a 57 mm inner ring diameter could be built using 32 of these detector modules. The average intrinsic spatial resolution in Y and X were 0.84 mm and 0.72 mm FHWM, respectively. There was a 28% miscoding error in X, mainly from Compton scatter in the crystal array. The Z or depth of interaction (DOI) resolution is 1.74 mm. The intrinsic spatial resolution is reasonably uniform across the whole detector module.