We report on the low-energy dynamics in the kagome antiferromagnet CaCu3(OD)6Cl2·0.6D2O (Ca-kapellasite) as studied by use of 2D-NMR measurements. Previous 35Cl-NMR measurements revealed that the nuclear spin-lattice relaxation rate (1=T1) shows two peaks at temperatures, T∗ = 7.2K and Ts ≃ 25 K. While the low-temperature peak at T∗ is ascribed to the critical fluctuations near the long-range magnetic ordering, the origin of the high-temperature peak has not been fully understood. From the 1=T1 measurements on the D sites at the OD groups (DOD), we find no peak at Ts, evidencing that the high-temperature peak is not related to the molecular dynamics of the OD groups. We discuss the possibility of a frustration-induced short-range ordered state below Ts before the long-range order is stabilized by the Dzyaloshinskii-Moriya interaction. We also observed static internal fields at the DOD site in the long-range ordered state below T∗, and confirm the previously proposed negative-chirality q = 0 magnetic structure.