Abdominal auscultation is a convenient, safe and inexpensive method to assess bowel conditions, which is essential in neonatal care. It helps early detection of neonatal bowel dysfunctions and allows timely intervention. This paper presents a neonatal bowel sound detection method to assist the auscultation. Specifically, a Convolutional Neural Network (CNN) is proposed to classify peristalsis and non-peristalsis sounds. The classification is then optimized using a Laplace Hidden Semi-Markov Model (HSMM). The proposed method is validated on abdominal sounds from 49 newborn infants admitted to our tertiary Neonatal Intensive Care Unit (NICU). The results show that the method can effectively detect bowel sounds with accuracy and area under curve (AUC) score being 89.81% and 83.96% respectively, outperforming 13 baseline methods. Furthermore, the proposed Laplace HSMM refinement strategy is proven capable to enhance other bowel sound detection models. The outcomes of this work have the potential to facilitate future telehealth applications for neonatal care. The source code of our work can be found at: https://bitbucket.org/chirudeakin/neonatal-bowel-sound-classification/