This paper demonstrates that, for large-scale tests, the match and non-match similarity scores have no specific underlying distribution function. The forms of these distribution functions require a nonparametric approach for the analysis of the fingerprint similarity scores. In this paper, we present an analysis of the discrete distribution functions of the match and non-match similarity scores of the fingerprint data that clarifies the widely varying form of these distribution functions. This analysis demonstrates that a precise Receiver Operating Characteristic (ROC) curve based on the True Accept Rate (TAR) of the match similarity scores and the False Accept Rate (FAR) of the non-match similarity scores can be constructed without any assumption regarding operating thresholds or the form of the distribution functions. The area under such a ROC curve, assuming normality, is equivalent to the Mann-Whitney statistic directly formed from the match and non-match similarity scores. In addition, the Z statistic computed using the areas under ROC curves along with their variances is applied to test the significance of the difference between two ROC curves. Four examples than from NIST's extensive testing of commercial fingerprint systems are provided. The nonparametric approach presented in this article can also be employed in the analysis of other biometric data.