The spontaneous cerebral activity that gives rise to resting-state networks (RSNs) has been extensively studied in infants in recent years. However, the influence of sleep state on the presence of observable RSNs has yet to be formally investigated in the infant population, despite evidence that sleep modulates resting-state functional connectivity in adults. This effect could be extremely important, as most infant neuroimaging studies rely on the neonate to remain asleep throughout data acquisition. In this study, we combine functional near-infrared spectroscopy with electroencephalography to simultaneously monitor sleep state and investigate RSNs in a cohort of healthy term born neonates. During active sleep (AS) and quiet sleep (QS) our newborn neonates show functional connectivity patterns spatially consistent with previously reported RSN structures. Our three independent functional connectivity analyses revealed stronger interhemispheric connectivity during AS than during QS. In turn, within hemisphere short-range functional connectivity seems to be enhanced during QS. These findings underline the importance of sleep state monitoring in the investigation of RSNs.