Hypotension or low blood pressure (BP) is a common problem in preterm neonates and has been associated with adverse short and long-term outcomes. Deciding when and whether to treat hypotension relies on an understanding of the relations between blood pressure and brain function. This study aims to investigate the interaction between BP and multichannel EEG in preterm infants less than 32 weeks gestational age. The mutual information is chosen to model interaction. This measure is independent of absolute values of BP and electroencephalography (EEG) power and quantifies the level of coupling between the short-term dynamics in both signals. It is shown that while adverse health conditions as measured by higher clinical risk indices for babies (CRIB II) are accompanied by consistently lower blood pressure (r=0.43), no significant correlation was observed between CRIB scores and EEG spectral power. More importantly, the chosen measure of interaction between dynamics of EEG and BP was found to be more closely related to CRIB scores (r=0.49, p-value=0.012), with higher CRIB score associated with lower levels of interaction.