Program slicing is a reduction technique that removes irrelevant parts of a program automatically, based on dependencies. It is used in the context of documentation to improve the user's understanding as well as for reducing the size of a program when analysing. In this paper we describe an approach for slicing not program code but models of software or systems written in the graphical Behavior Tree language. Our focus is to utilise this reduction technique when model checking Behavior Tree models. Model checking as a fully automated analysis technique is restricted in the size of the model and slicing provides one means to improve on the inherent limitations. We present a Health Information System as a case study. The full model of the system could not be verified due to memory limits. However, our slicing algorithm renders the model to a size for which the model checker terminates. The results nicely demonstrate and quantify the benefits of our approach.