Parkinson disease (PD) patients with rapid eye movement (REM) sleep behavior disorder (RBD) have worse motor symptoms and non-motor symptoms than patients without RBD. The aim of this study was to examine underlying differences in brain structure from a network perspective. Baseline data were obtained from Parkinson's Progression Markers Initiative (PPMI) participants. We divided PD patients and healthy controls (HC) into RBD positive and RBD negative using a cutoff score of ≥5 on the RBD screening questionnaire. HC with probable RBD were excluded. We first carried out a region-of-interest analysis of structural MRIs using voxel-based morphometry to study volumetric differences for the putamen, thalamus and hippocampus in a cross-sectional design. Additionally, an exploratory whole-brain analysis was performed. To study group differences from a network perspective, we then performed a 'seed-based' analysis of structural covariance, using the bilateral dorsal-caudal putamen, mediodorsal thalamus and anterior hippocampus as seed regions. The volume of the right putamen was smaller in PD patients with RBD. RBD symptom severity correlated negatively with volume of the right putamen, left hippocampus and left thalamus. We did not find any differences in structural covariance between PD patients with and without RBD. Presence of RBD and severity of RBD symptoms in PD are associated with smaller volumes of the putamen, thalamus and hippocampus.