The large volume and nature of data available to the casual users and programs motivate the increasing interest of the database community in studying flexible and efficient techniques for extracting and querying semistructured data. On the other hand, efficient methods have been discovered for solving the so-called model-checking problem for some modal logics. The aim of this paper is to show how some of these methods can be used for querying semistructured data. For doing that we show that semistructured data can be naturally seen as Kripke Transition Systems. To keep the presentation independent of a specific language, we introduce a graphical query language that includes some of the features of the query languages based on graphs and patterns. We show how to associate CTL formulas to queries of this language. This allows us to see the problems of solving a query as an instance of the model-checking problem for CTL that can be solved in polynomial time. We have tested the method by using a model-checker, and have studied the applicability of the method to some existing languages for semistructured databases.