Autonomous robots operating in real-world environments encounter a variety of objects that can be both rigid and articulated in nature. Having knowledge of these specific object properties not only helps in designing appropriate manipulation strategies but also aids in developing reliable tracking and pose estimation techniques for many robotic and vision applications. In this context, this paper presents a registration-based local region-to-region mapping approach to classify an object as either articulated or rigid. Using the point clouds of the intended object, the proposed method performs classification by estimating unique local transformations between point clouds over the observed sequence of movements of the object. The significant advantage of the proposed method is that it is a constraint-free approach that can classify any articulated object and is not limited to a specific type of articulation. Additionally, it is a model-free approach with no learning components, which means it can classify whether an object is articulated without requiring any object models or labelled data. We analyze the performance of the proposed method on two publicly available benchmark datasets with a combination of articulated and rigid objects. It is observed that the proposed method can classify articulated and rigid objects with good accuracy.