The paper presents results of a sleep study on 60 newborn infants and 22 one-month infants, in quiet and active sleep and in prone and supine position. During the study, HRV and respiration were acquired and then analyzed with a multi-parametric approach. Time, Frequency Domain and Non-Linear parameters were calculated, also encompassing indices from the adult and fetal field. The novelty of this study is the introduction of innovative measurements in a thorough investigation to characterize the effect of sleep state and position on the cardio-respiratory control in newborns. Results show that most parameters succeed in classifying different sleep states, while differences between positions were found in the one-month population only. This study comes as a continuation of previous analysis with the addition of respiratory signal. These results are encouraging for the aim of defining a set of parameters that could help characterizing the autonomic control of infants and early detect the onset of distress or particular pathologies.