Data generated from some deterministic dynamical systems may appear random. This phenomenon is called chaos. Many classical test statistics cannot distinguish this type of data from IID random observations. Recently, some new test statistics based on correlation integrals were proposed in the literature. However, the statistical properties of these new test statistics have not been studied. This paper studies the asymptotic properties of these test statistics under the IID null hypothesis. Establishing the asymptotic distributions of the test statistics facilitates statistical hypothesis testing. The asymptotic null distributions derived are supported by Monte Carlo simulations.