To understand the behaviors of an individual, it is crucial to understand the neural connections of the nervous system, that is, the connectome. The hermaphrodite Caenorhabditis elegans connectome has served as a prototype for analytical studies since the chemical synapses and gap junctions among the 302 neurons were completely mapped. Recently, monoamine (MA) and neuropeptide (NP) connections were established, which form a multilayer connectome in conjunction with chemical synapses and gap junctions. In this study, we investigated the difference in the in-degree and out-degree distributions, respectively, among the connectomes with and without MA and NP connections. We found that the in-degree and out-degree distributions show different properties of dissimilarity. We discovered that only a few of the degree distributions can be fitted perfectly to power-law or exponential models. Finally, clustering analysis suggests that MA and NP connections significantly alter the degree distributions of the C. elegans connectome. Overall, our study provides an insight into the structural properties of the multilayer connectome with MA and NP connections and confirms the necessity to investigate the multilayer connectome to understand the behaviors of a worm.