The rotational dynamics of the hexafluorophosphate anion (PF6-) in the crystalline and liquid states of the archetypal room temperature ionic liquid (RTIL) 1-butyl-3-methylimidazolium hexafluorophosphate ([C(4)mim]PF6) are investigated using P-31 NMR spectroscopy line shape analyses and spin-lattice relaxation time measurements. The PF6- anion performs isotropic rotation in all three polymorphic crystals phases alpha, beta, and gamma as well as in the liquid state with a characteristic time scale that ranges from a few ps to a few hundred ps over a temperature range of 180-280 K. The rotational correlation time tau(c) for PF6- rotation follows the sequence gamma-phase < alpha-phase approximate to liquid < beta-phase. On the other hand, in the liquid state, all local motions in the cation as well as its global rotational reorientation are characterized by time scales that are slower compared to that for the PF6- anion rotation. The time scale tau(c) and the activation energy of PF6- rotation in this RTIL are found to be comparable with those observed in ordinary alkali and ammonium salts despite the large counterion size and low melting point of the former. The high sphericity of the PF6- ion is hypothesized to play an important role in the decoupling of its rotational dynamics that appear to be practically independent of the averaged cation-anion interaction.