The quasi-1D conductor (TMTSF)
2PF
6, has a Spin Density Wave transition at 12 K. Previous H
1 NMR studies have shown that the spin-lattice relaxation rate, T
1, is finite and Korringa-like inside the Spin Density Wave phase down to about 4 K below which T
1 increases rapidly. We have measured the linewidth, T
1 and the spin-spin relaxation time, T
2, of the e
77Se nuclei which, as calculated by bandstructure, are in closer physical proximity to the electron conduction paths than the H
1 and, consequently, more strongly coupled to the conduction electrons. Using fields up to 24 T, we find that while the lineshape is temperature independent inside the SDW phase, the e
77Se T
1 exhibits the same qualitative behavior as the H
1 T
1, and T
2 increases abruptly at
4 K. We discuss this result in terms of the Fermi surface of the system.