We present Atacama Compact Array and Atacama Pathfinder Experiment observations of the [N II] 205 mu m fine-structure line in 40 sub-millimetre galaxies lying at redshifts z = 3-6, drawn from the 2500 deg(2) South Pole Thlescope survey. This represents the largest uniformly selected sample of high-redshift [N II] 205 mu m measurements to date. 29 sources also have [C II] 158 mu m line observations allowing a characterization of the distribution of the [C II] to [N II] luminosity ratio for the first time at high redshift. The sample exhibits a median L[C II] /L [N II]) approximate to 11.0 and interquartile range of 5.0 -24.7. These ratios are similar to those observed in local (Ultra)luminous infrared galaxies (LIRGs), possibly indicating similarities in their interstellar medium. At the extremes, we find individual sub-millimetre galaxies with L[C II]/L [N II] low enough to suggest a smaller contribution from neutral gas than ionized gas to the [C II] flux and high enough to suggest strongly photon or X-ray region dominated flux. These results highlight a large range in this line luminosity ratio for sub-millimetre galaxies, which may be caused by variations in gas density, the relative abundances of carbon and nitrogen, ionization parameter, metallicity, and a variation in the fractional abundance of ionized and neutral interstellar medium.