It is well known that the coordination among several subsystems in newborns is effectively changing as a function of behavioral states. For this reason, sleep state characterization is an essential procedure in neonatal monitoring. Despite its importance, methodologies assessing sleep states are discrete in time and usually based on visual inspection. In this work, we validate a point process framework on a population of 113 full-term infants with the aim of providing continuous sleep state characterization over time. After determining a suitable probability density distribution to best fit the neonatal RR series, we compare traditional heart rate variability (HRV) parameters with the point process-extracted sets of time and frequency domain instantaneous measures in order to validate the proposed framework. Our results provide insights into the point process ability to capture HRV dynamics with a high degree of reliability, thus providing evidence that our framework might be employed for an instantaneous estimate of behavioral states.