Cardiorespiratory interaction (CRI) has been intensively studied in adult sleep, yet not in preterm infants, in particular across different sleep states including wake (W), active sleep (AS), and quiet sleep (QS). The aim of this study was to quantify the interaction between cardiac and respiratory activities in different sleep states of preterm infants. The postmenstrual age (PMA) of preterm infants was also taken into consideration. The CRI during sleep was analyzed using a visibility graph (VG) method, enabling the nonlinear analysis of CRI in a complex network. For each sleep state, parameters quantifying various aspects of the CRI characteristics from constructed VG network including mean degree (Dm) and its variability (Dsd), clustering coefficient (CCm) and its variability (CCsd), assortativity coefficient (AC) and complexity (DSE) were extracted from the CRI networks. The interaction effect of sleep state and PMA was found to be statistically significant on all CRI parameters but AC and DSE. The main effect between sleep state and CRI parameters was statistically significant except for CCm, and that between PMA and CRI parameters was statistically significant but DSE. In conclusion, the CRI of preterm infants is associated with sleep states and PMA in general. For preterm infants with a larger PMA, CRI has a more clustered pattern during different sleep states, where QS shows a more regular, stratified, and stronger CRI than other states. In the future, these parameters can be potentially used to separate sleep states in preterm infants.