Recursive state machines (RSMs) are state-based models for procedural programs with wide-ranging applications in program verification and interprocedural analysis. Model-checking algorithms for RSMs and related formalisms and various temporal logic specifications have been intensively studied in the literature. In this paper, we devise a new model-checking algorithm for RSMs and requirements in computation tree logic (CTL) that exploits the compositional structure of RSMs by ternary model checking in combination with a lazy evaluation scheme. Specifically, a procedural component is only analyzed in those cases in which it might influence the satisfaction of the CTL requirement. We evaluate our prototypical implementation on randomized scalability benchmarks and on an interprocedural data-flow analysis of Java programs, showing both practical applicability and significant speedups in comparison to state-of-the-art model-checking tools for procedural programs.