States aren’t something natively supported in C++ in the same way that Unrealscript supported them. I’d tend to say the closest equivalent is the state machine design pattern, wherein you encapsulate the state-specific logic into a series of classes inheriting from a common parent, and have your object store a reference to the base class that you can then instantiate specific states into, to utilise virtual functions.
From a quick glance, State · Design Patterns Revisited · Game Programming Patterns seems to have a reasonable explanation of the concept.