The spin-lattice relaxation times T-1 for H-2 and N-14 of acetonitrile-d(3)(CD3CN) are measured in pure liquid, n-hexane, carbon tetrachloride, acetone, methanol, water, and heavy water as functions of temperature and concentration. From the T-1 values, the rotational diffusion coefficients for the tumbling and spinning motions are separately obtained. The tumbling motion is strongly dependent on the solvent and temperature and its diffusion coefficient is qualitatively explained by a simple dielectric friction model. The spinning motion is, on the other hand, weakly dependent on the solvent and temperature. The observed large anisotropy ratio (similar to 9) of the spinning to the tumbling modes represents the anisotropy of the solvation shell and is explained by neither the free rotor model nor the hydrodynamic continuum model. The tumbling motion is more strongly hindered than the spinning motion due to the dipolar interaction between the solute and solvent.