We study the use of Predictive State Representation (PSR) for modeling of an in-hand manipulation task through interaction with the environment. We extend the original PSR model to a new domain of in-hand manipulation and address the problem of partial observability by introducing new kernel-based features that integrate both actions and observations. The model is learned directly from haptic data and is used to plan series of actions that rotate the object in the hand to a specific configuration by pushing it against a table. Further, we analyze the model's belief states using additional visual data and enable planning of action sequences when the observations are ambiguous. We show that the learned representation is geometrically meaningful by embedding labeled action-observation traces. Suitability for planning is demonstrated by a post-grasp manipulation example that changes the object state to multiple specified target configurations.