In this article, we report the temperature dependence of spin-lattice relaxation rates at two Pt sites and one Si site in CePt3Si with a non-centrosymmetric structure center. 1/T1 for both Pt sites between 2 K and 300 K and 1/T1 of Si above 3 K might be explained by the contributions from the low-lying crystal-electric-field level and the quasiparticle due to the hybridization between the ground state and conduction electrons. Just below Tc no remarkable enhancement in 1/T1 was observed. The estimated value of superconducting gap is about 2Delta = 3kBTc.
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