The Clock Constraint Specification Language (CCSL) provides expressions and relations to specify the time requirements and causal dependencies of systems. It was initially proposed, in the context of MARTE: the UML profile for Modeling and Analysis of Real-Time and Embedded Systems. In this paper, we propose a method to verify CCSL specifications. We give a formal state-based interpretation of a fundamental subset of CCSL clock constraints. Based on it, we translate a CCSL specification into a Promela model and feed the result into the model checker SPIN. Then we show some patterns for expressing the properties of the model and do the verification. A digital filter application is used as an example to illustrate the approach.