The inorganic Cs I(Tl) crystal scintillator is a candidate anti-compton detector for the China Dark matter Experiment. Studying the intrinsic radiopurity of the Cs I(Tl) crystal is an issue of major importance. The timing,energy and spatial correlations, as well as the capability of pulse shape discrimination provide powerful methods for the measurement of intrinsic radiopurities. The experimental design, detector performance and event-selection algorithms are described. A total of 359×3 kg-days data from three prototypes of Cs I(Tl) crystals were taken at China Jinping Underground Laboratory(CJPL), which offers a good shielding environment. The contamination levels of internal isotopes from137 Cs,232Th and238 U series, as well as the upper bounds of235 U series are reported.Identification of the whole α peaks from U/Th decay chains and derivation of those corresponding quenching factors are achieved. The intrinsic Cs (Tl) crystal scintillator is a candidate anti-compton detector for the China Dark matter Experiment. The timing, energy and spatial correlations, As well as the capability of pulse shape discrimination provide powerful methods for the measurement of intrinsic radiopurities. The experimental design, detector performance and event-selection algorithms are described. A total of 359 × 3 kg-days data from three prototypes of Cs I ( Tl) crystals were taken at China Jinping Underground Laboratory (CJPL), which offers a good shielding environment. The contamination levels of internal isotopes from 137 Cs, 232 Th and 238 U series, as well as the upper bounds of 235 U series are reported. Identification of the whole alpha peaks from U / Th decay chains and derivation of each corresponding quenching factors are achieved.