In the field of human-robot interaction (HRI), social coordination, meaning the cooperation between humans and robots through emotional and cognitive states, can be an essential element in considering the social position of robots for social implementation. A handshake is an interaction involving physical and social coordination in that it is the first interaction between humans involving physical contact, but also the first opportunity for social interaction. In this paper, we developed a CPG (Central Pattern Generator) controlled handshake robot to clarify the relationship between this social and physical coordination. In the experiment, we investigated how the control method affects the robot’s social attributes as perceived by humans by using the Robot Social Attributes Scale (RoSAS) for passive control methods using simple impedance control and cooperative and active control methods using the CPG controller we developed. Results from a 14-subject experiment showed that the CPG-based control method improved the social attributes of being competent and comfortable with the robot. Based on the results of these studies, we propose guidelines for future research on handshake robots and contribute to the development of future social robots.