Touch displays moving autonomously, i.e., being selfactuated, are starting to be part of system prototypes reported in the literature. In the future, user interactions with such prototypes may take place while the display is moving. However, since current prototypes do not yet require this type of interaction, there is a lack of empirical evidence reporting issues related to touch input in such conditions. This leads us to propose two basic questions: Can we request users to deliver touch gestures during the actuation? Which aspects should we take into account when having touch input in these moving devices? In order to start to answer these questions, we report in this paper a first study to get an insight into how people perform and feel it when they have to carry out touch input on a self-actuated tablet. The preliminary results show that the self-actuated tablet does not necessarily need to be still during touch interaction, and that single-touch gestures based on drag or tap are preferable over others. Furthermore, the results also revealed an issue with tap gestures because of the movement of the tablet.