Multi-Agent Path Finding has been widely studied in the past few years due to its broad application in the field of robotics and AI. However, previous solvers rely on several simplifying assumptions. They limit their applicability in numerous real-world domains that adopt nonholonomic car-like agents rather than holonomic ones. In this paper, we give a mathematical formalization of Multi-Agent Path Finding for Car-Like robots (CL-MAPF) problem. For the first time, we propose a novel hierarchical search-based solver called Car-like Conflict-Based Search to address this problem. It applies a body conflict tree to address collisions considering shapes of the agents. We introduce a new algorithm called Spatiotemporal Hybrid-State A* as the single-agent path planner to generate path satisfying both kinematic and spatiotemporal constraints. We also present a sequential planning version of our method for the sake of efficiency. We compare our method with two baseline algorithms on a dedicated benchmark containing 3000 instances and validate it in real-world scenarios. The experiment results give clear evidence that our algorithm scales well to a large number of agents and is able to produce solutions that can be directly applied to car-like robots in the real world. The benchmark and source code are released in https://github.com/APRIL-ZJU/CL-CBS.