Computer aided diagnosis (CAD) in medical imaging is of growing interest in recent years. Our proposed CAD system aims to enhance diagnosis and prognosis of traumatic brain injury (TBI) patients with hematomas. Hematoma caused by blood vessel rupture is the major lesion in TBI cases and is usually assessed using head computed tomography (CT). In our CAD system, we segment the hematoma region from each slice of a CT series, extract features from the hematoma segments, and automatically classify the hematoma types using machine learning methods. We propose two sets of shape based features for each segmented hematoma region. The first set contains primitive features describing the overall shape of a hematoma region. The features in the second set are based on the dissimilarities of the shapes of hematoma regions measured by geodesic distances. After feature extraction, we classify the hematoma regions into three types -- epidural hematoma, sub-dural hematoma, and intracerebral hematoma, using random forest. Each tree of the random forest votes one class for each hematoma, and the random forest takes the class label with the majority votes for the hematoma. As hematomas are volumetric in nature, some hematomas are observed across several consecutive slices in the same CT series. For each class, we add the votes from each hematoma slice that comprises the volumetric hematoma in that class, then we take the class with the majority of the summed votes as the class label for that volumetric hematoma. The overall classification accuracies for hematoma region from each CT slice are 80.7%, 81.3%, and 81.1% using primitive features only, geodesic distance features only, or both sets of features, respectively. For volumetric hematoma classification, the overall accuracies are 80.9%, 81.5%, and 81.5% respectively. The results are promising to radiologists and neurosurgeons specialized in this field of research.