Concolic testing is a well-known validation technique for imperative and object-oriented programs. We have recently introduced an adaptation of this technique to logic programming. At the heart of our framework for concolic testing lies a logic programming specific procedure that we call "selective unification". In this paper, we consider concolic testing in the context of constraint logic programming and extend the notion of selective unification accordingly. We prove that the selective unification problem is generally undecidable for constraint logic programs, and we present a correct and complete algorithm for selective unification in the context of a class of constraint structures.