The spin-lattice relaxation time, T1, and the self-diffusion coefficient, D, have been measured in carbon dioxide near the critical point. T1 values are the first for CO2 and this is the third D determination in the critical region. The two previous D determinations, a tracer study conducted by Harris and Duffield (1976) [14] and an NMR study conducted by Krynicki et al. (1981) [20] are in serious disagreement. Harris reported the presence of a strong critical anomaly whereas Krynicki observed that D behaves normally in the critical region. Two isotherms were investigated, 31.06-degrees-C and 31.5-degrees-C in the density range 0.05rho(c)-1.5rho(c). No critical anomaly was found for either T1 or D. This confirms earlier findings on various gases and is in agreement with Krynicki's conclusions but stands in contradiction to the findings of Harris. We also had visual confirmation of the approach to the critical point via a sapphire cell connected to the NMR high-pressure probe. The ensemble, NMR probe and sapphire cell, were enclosed in a temperature-controlled air bath.