Increasing attention has recently been devoted to the multidisciplinary investigation of functional brain-heart interplay (BHI), which has provided meaningful insights in neuroscience and clinical domains including cardiology, neurology, clinical psychology, and psychiatry. While neural (brain) and heartbeat series show high nonlinear and complex dynamics, a complexity analysis on BHI series has not been performed yet. To this end, in this preliminary study, we investigate BHI complexity modulation in 17 healthy subjects undergoing a 3-minute resting state and emotional elicitation through standardized image slideshow. Electroencephalographic and heart rate variability series were the inputs of an adhoc BHI model, which provides directional (from-heart-to-brain and from-brain-to-heart) estimates at different frequency bands. A Fuzzy entropy analysis was performed channel-wise on the model output for the two experimental conditions. Results suggest that BHI complexity increases in the emotional elicitation phase with respect to a resting state, especially in the functional direction from the heart to the brain. We conclude that BHI complexity may be a viable computational tool to characterize neurophysiological and pathological states under different experimental conditions.