Spinal imaging serves as an invaluable tool in the non-invasive visualization and evaluation of spinal pathologies. A key basis for quantitative medical image analysis pertinent to clinical diagnosis and spinal surgery planning is the segmentation of vertebrae in computed tomography (CT) images. While fully convolutional networks in general dominate over medical image segmentation, with the U-Net being the architecture of choice, alternative methodologies may offer potential advancements. One promising approach is the deep implicit statistical shape model (DISSM), known for generating high-quality surfaces without discretization and for its robustness, underpinned by the use of rich and explicit anatomical priors, particularly for challenging cross-dataset clinical samples. This paper explores the utilization of DISSM for vertebra segmentation on two image datasets: a collection of 1005 CT spine images known as CTSpine1K for the shape decoder, and a set of 319 CT images known as VerSe2020 for the pose estimation encoders (translation, rotation, scaling and principal component analysis). These images and their corresponding vertebra segmentations are used for the preparation, preprocessing, and training and testing of DISSM. The preprocessing and learning techniques are based on a DISSM software package (AshStuff/dissm) with our custom modifications. The obtained segmentation results yielded an overall mean Dice coefficient of 0.767, average symmetric surface distance of 1.93 mm, and 95^th percentile Hausdorff distance of 5.71 mm. We can therefore conclude that DISSM has the potential to further advance the field of vertebra segmentation.