The accurate identification of sleep states in the fetal period is a necessary step to conduct accurate and reliable analyses of fetal heart rate variability (HRV). Currently, the assessment of the fetal sleep stages is usually performed by visual inspection, resulting in a time consuming and highly subjective procedure. In this work, we proposed a methodology for the automated identification of fetal sleep states, uniquely based on the analysis of features extracted from the fetal heart rate signal. Abdominal fetal ECG recordings were collected in a cohort of 66 pregnant women during the third trimester of gestation. Traces were acquired overnight at a sampling frequency equal to 300 Hz using the MonicaAN24 device. In this study, we analyzed 459 segments of 3-min duration extracted from the available data. A set of features was computed for each epoch, two time domain parameters, namely Short Term Variability (STV) and Long Term Irregularity (LTI), and a Phase Rectified Signal Averaging (PRSA)-derived index called Acceleration Capacity (AC). We combined the described indices to train different logistic regressions for the predicting of fetal states. The best performing model included a combination of two features, name LTI and the AC and achieved an accuracy = 0.88 and 0.87, sensitivity = 0.81 and 0.78, and specificity = 0.91 and 0.90 in discriminating the active (1F) and the quiet (2F) fetal states (considering 1F as the positive class), when tested on the training and testing tests, respectively. We employed a leave-one-subject-out validation schema. In this work, we provide evidence for the successful application of PRSA-derived features in the context of fetal sleep state classification. Specifically, the model trained on AC as standalone feature outperformed the ones employing STV and LTI alone, and the combination of AC and LTI yielded the best performance in the tested dataset.