The use of bistable laminates is a potential approach to realize more broadband piezoelectric based energy harvesting systems. Based on the experimental time series of a bistable laminate plate we have examined its dynamic response. The system was subjected to harmonic excitations showing the existence of single well and snap-through vibrations of periodic and chaotic character. To identify the dynamics of the system response we examine the frequency spectrum, phase portraits and multi-scaled entropy. It is observed that the composite multiscale entropy analysis can be used to identify complexity within the dynamic response successfully.