The assessment of fetal heart rate variability (FHRV) is fundamental for evaluating fetal well-being during pregnancy. Through cardiotocography (CTG), it is possible to monitor both the fetal heart rate (FHR) and the uterine contractions (UC) and, through the use og computerized analysis, it is also possible to extract synthetic parameters of the FHRV. Among the available FHRV indices, the use of symbolic dynamics (SD) arises as a promising nonlinear indicator to investigate the complexity in FHRV signals. However, there is not enough evidence of the reliability of such indices and no consensus on the proposed formula to compute them. Based on previous works on this topic, here we aim at carrying out a sensitivity analysis of one of the proposed SD parameters for FHRV analysis, namely the Variability Index (VI). A database of 583 CTG signals has been used as basis for this study. The signals were preprocessed and analyzed to extract the FHRV series and calculate the VI according to a predefined set of weights. Then, the weights have been systematically varied and the sensitivity of the obtained VI in discriminating different fetal conditions and signal characteristics was assessed by means of a statistical approach. The results obtained show that the choice of weights can be decisive for specific purposes, e.g. in evaluating fetal development and distinguishing cesarean from spontaneous sections. On the other hand, weights do not alter the VI sensitivity in discriminating between active and rest states, presence and absence of accelerations.