Over the last years, a number of different path following methods for the autonomous parking system have been proposed for tracking planned paths. However, it is difficult to find a study comparing path following methods for a short path length with large curvature such as a parking path. In this paper, we conduct a comparative study of the path following methods for perpendicular parking. By using Monte-Carlo simulation, we determine the optimal parameters of each controller and analyze the performance of the path following. In addition, we consider the path following error occurred at the switching point where forward and reverse paths are switched. To address this error, we conduct the comparative study of the path following methods with the one thousand switching points generated by the Monte-Carlo method. The performance of each controller is analyzed using the V-rep simulator. With the simulation results, this paper provides a deep discussion about the effectiveness and limitations of each algorithm.