Complexity measures from Multiscale Entropy (MSE) analysis of cardiovascular variability may provide potential biomarkers of pathological mental states such as major depression. To this extent, in this study we investigate whether complexity of Heart Rate Variability (HRV) is also affected in mental disorders such as bipolar disorders (BD). As part of the European project PSYCHE, eight BD patients experiencing multiple pathological mood states among depression, hypomania, and euthymia (i.e., good affective balance) underwent long-term night recordings through a comfortable sensing t-shirt with integrated fabric electrodes and sensors. Standard radius, i.e., 20% of the HRV standard deviation, and a maximal-radius choice for the sample entropy estimation were compared along with a further multiscale Renyi Entropy analysis. We found that, despite the inter-subject variability, the maximal-radius MSE analysis is able to discern the considered pathological mental states of BD. As the current clinical practice in diagnosing BD is only based on verbal interviews and scores from specific questionnaires, these findings provide evidence on the possibility of using heartbeat complexity as the basis of novel clinical biomarkers of mental disorders.