New production vehicles equipped with multiple screens have various functions and technologies at the user's fingertips that create informative and immersive cockpits not only for the driver but also for the passenger. Despite the growing popularity of the co-pilot display, surprisingly little is known about the impact of its engagement on drivers. Engagement, in the context of this paper, is defined as visual, auditory, and mental involvement but no manual involvement. The present study sought to investigate the effects of co-pilot display engagement on drivers' visual workload, cognitive workload, and driving performance and offered a deeper insight into the design factors and task involvement of the co-pilot display. The study involved a driving simulator testing of 25 participants in five automobiles with a co-pilot display. Our analysis found increased driver visual workload and cognitive workload in the conditions of co-pilot display engagement. Participants exhibited more erratic driving behavior (standard deviation of speed and standard deviation of lane position) while the front passenger was watching a video. Furthermore, five linear mixed models were built to further analyze the effects of task type, screen size, screen layout, and task involvement on dependent measures. Potential applications of this research include refinements to the co-pilot display and workload estimation of co-pilot display engagement.