To evaluate and assess the cardiovascular system during fetal development in the utero of pregnant mouse, it is essential to understand the effect of mandatory anesthesia treatment on sympathetic and parasympathetic nervous system activities. The preliminary study presented in this paper explores the changes in fetal and maternal Heart Rate Variability (HRV) parameters as well as fetal-maternal Heart Rate (HR) coupling measures during anesthesia. ECG signals of 6 pregnant mice and 10 fetuses were recordedfor 15 min. The obtained ECG signals were segmented into three periods, each for a duration of 5 min. Maternal and fetal HRV parameters in addition to fetal-maternal coupling patterns were computed for each of the three segments of the ECG signals. During the first 10 min, results show that mean and root mean square of successive differences (RMSSD) of maternal HR did not change, but significantly decreased after the first 10 min. A similar result was observed for the mean, RMSSD and standard deviation of NN intervals in fetal HR. On the other hand, no significant changes were observed for the coupling patterns between fetal-maternal heartbeats. These observations suggest that fetal nervous system activities were suppressed by anesthesia treatment applied to pregnant mice for more than 10 min.