Parkinson’s disease (PD) is associated with cognitive and sleep impairments. The presence of rapid eye movement (REM) sleep behavior disorder (RBD) symptoms may represent a worse disease prognosis for PD individuals. We investigated cognitive functioning and self-reported sleep in early-stage PD individuals with (n = 19) or without (n = 31) probable RBD. Probable RBD was defined as >5 on the REM Sleep Behavior Disorder Screening Questionnaire. Inhibition, visuospatial cognitive abilities, working memory, sustained visual attention, verbal fluency, and episodic memory were assessed. Sleep impairments were assessed using the Pittsburgh Sleep Quality Index, Insomnia Severity Index, Epworth Sleepiness Scale, and Patient-Reported Outcomes Measurement Information System questionnaires. Chi-squared, Mann-Whitney U, and independent sample t-tests were employed to assess group differences. Participants with PD and probable RBD performed significantly worse on word reading and switching verbal fluency tasks than PD participants without probable RBD (p < 0.05). No significant differences were found in mood, PD severity, or sleep measures between PD individuals with or without probable RBD. Cognitive tasks that involve verbal or switching components may be most impaired in PD individuals with probable RBD. Larger samples are needed to determine whether other cognitive domains and sleep features are significantly associated with RBD in PD.