In respect to the main goal of our ongoing work for predicting preterm birth, we analyze in this paper uterine EMG recordings of 11 pregnant and laboring women by means of Detrended Fluctuation Analysis (DFA), a scaling analysis method that quantifies a simple parameter to represent the correlation properties of a time series. Our study provides convincing evidence that pregnancy progress is typically associated to an alteration in the long-range correlation of the uterine EMG recordings. The results obtained from the analyzed data indicate that the correlation in the contractions increases during pregnancy. Furthermore, we demonstrate that the long-range parameter may discriminate between the two classes (pregnancy/labor). The results are supported by statistical analysis using t-test indicating good statistical significance with a confidence level of 95%. A surrogate data test is also performed to investigate the nature of the underlying dynamics of our experimental data. The results are very promising for monitoring pregnancy and detecting labor and may help identify preterm labor.