Constraint-logic object-oriented programming facilitates the integrated development of business software that occasionally solves constraint-logic problems or makes other use of structured search. So far, work in constraint-logic object-oriented programming has been limited to considering constraints that only involve logic variables of primitive types; in particular, boolean, integer, and floating-point numbers. However, the availability of object-oriented features calls for the option to use logic variables in lieu of objects as well. Therefore, support for reference-type logic variables (or free objects) is required. With the work at hand, we add support for free objects to a Java-based constraint-logic object-oriented language, Muli. Allowing free objects in statements and expressions results in novel interactions with objects at run time, for instance, non-deterministic execution of polymorphic method invocations (taking arbitrary class hierarchies into account) and non-deterministic type operations. At run time, this is supported by a dynamic type constraint that restricts the possible types of a free object at non-deterministic choices.