The inorganic crystal scintillator CsI(Tl) has been used for low energy neutrino and Dark Matter experiments, where the intrinsic radiopurity is an issue of major importance. Low-background data were taken with a CsI(Tl) crystal array at the Kuo-Sheng Reactor Neutrino Laboratory. The pulse shape discrimination capabilities of the crystal, as well as the temporal and spatial correlations of the events, provide powerful means of measuring the intrinsic radiopurity of 137 Cs as well as the 235 U, 238 U and 232 Th series. The event selection algorithms are described, with which the decay half-lives of 218 Po, 214 Po, 220 Rn, 216 Po and 212 Po were derived. The measurements of the contamination levels, their concentration gradients with the crystal growth axis, and the uniformity among different crystal samples, are reported. The radiopurity in the 238 U and 232 Th series are comparable to those of the best reported in other crystal scintillators. Significant improvements in measurement sensitivities were achieved, similar to those from dedicated massive liquid scintillator detector. This analysis also provides in situ measurements of the detector performance parameters, such as spatial resolution, quenching factors, and data acquisition dead time.