The Turing test is an imitation game for determining the intelligence of an agent. In spite of its simplified setting, the use of natural language between two agents in the test is still too high a hurdle for achieving fruitful results in the field of artificial intelligence. In this paper, the authors propose a variation of the Turing test with a restricted communication method. This modified test uses behaviors generated by two-axis actuators for communication instead of the natural language dialogue used in the normal Turing test. This reduction of scope reveals what kinds of features are essential for an imitation game, and broaden the application brought by Turing test. When we learn what sorts of communication become possible with restricted actuation, we can apply this knowledge to any kind of robot or device in the real world. First, we tried to determine what elements are critical for communication between a user and a robot through a preliminary experiment involving human-human communication. A human manipulator received a video image as input and controlled a "robot box" with two actuators in a way that would lead a user to put other objects into the box. The results indicated what kinds of behavior are required to show the intention of the manipulator to the user. Second, we analyzed the result of the preliminary experiment, organized a behavioral model from the result, and programmed the robot box to run the model. The behavior of the robot was programmed according to the user's head and hand locations as identified by a motion captures system. The robot automatically interact with a human without human manipulation with this program. Third, we conducted a behavioral Turing test in a communication task whereby the human collected items according to the instructions of the robot box. In this test, two actuators on the box is controlled both by human manipulator and our program. The answers of users suggests that the users could not identify which is controlled by a human manipulator or the program. This result indicates that the Turing test succeed in a restricted behavioral level.