We present a novel collaborative mapping and autonomous parking system for semi-structured multi-story parking garages, based on cooperative 3-D LiDAR point cloud registration and Bayesian probabilistic updating. First, an inertial-enhanced (IE) generalized iterative closest point (G-ICP) approach is presented to perform high accuracy registration for LiDAR odometry, which is loosely coupled with inertial measurement unit using multi-state extended Kalman filter fusion. Second, the IE G-ICP is utilized to reconstruct the 3-D point cloud model for each vehicle, and then the individual model maps are merged and updated into a global probabilistic 2-D grid map. A collaborative multiple layer semantic map is constructed to support autonomous parking. Finally, we propose a collaborative navigation approach for path planning when there are multiple vehicles in the parking garage through vehicle-to-vehicle communication. A global path planner is designed to explore the minimum cost path based on the semantic map, and local motion planning is performed using a random exploring algorithm for obstacle avoidance and path smoothing. Our pilot experimental evaluation provides a proof of concept for indoor autonomous parking by collaborative perception, map merging, and updating methodologies.