Cd3As2 is a Dirac semimetal that is a 3D analog of graphene. We investigated the local structure and nuclear-spin dynamics in Cd3As2 via Cd-113 NMR. The wideline spectrum of the static sample at 295K is asymmetric and its features are well described by a two-site model with the shielding parameters extracted via Herzfeld-Berger analysis of the magic-angle spinning spectrum. Surprisingly, the Cd-113 spin-lattice relaxation time (T-1) is extremely long (T-1 = 95 s at 295 K), in stark contrast to conductors and the effects of native defects upon semiconductors; but it is similar to that of C-13 in graphene (T-1 = 110 s). The temperature dependence of 1/T-1 revealed a complex bipartite mechanism that included a T-2 power-law behavior below 330 K and a thermally activated process above 330 K. In the high-temperature regime, the Arrhenius behavior is consistent with a field-dependent Cd atomic hopping relaxation process. At low temperatures, a T-2 behavior consistent with a spin-1/2 Raman-like process provides evidence of a time-dependent spin-rotation magnetic field caused by angular oscillations of internuclear vectors due to lattice vibrations. The observed mechanism does not conform to the conventional two-band model of semimetals, but is instead closer to a mechanism observed in high-Z element ionic solids with large magnetorotation constant [A.J. Vega et al., Phys. Rev. B 74, 214420 (2006)/. Published by AIP Publishing.