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As part of a chemodynamical survey of five nearby globular clusters with 2dF/AAOmega on the Anglo-Australian Telescope (AAT), we have obtained kinematic information for the globular cluster NGC 3201. Our new observations confirm the presence of a significant velocity gradient across the cluster which can almost entirely be explained by the high proper motion of the cluster (${\sim}9\, \mathrm{mas\, yr^{-1}}$). After subtracting the contribution of this perspective rotation, we found a remaining rotation signal with an amplitude of ${\sim}1\, \mathrm{km\, s^{-1}}$ around a different axis to what we expect from the tidal tails and the potential escapers, suggesting that this rotation is internal and can be a remnant of its formation process. At the outer part, we found a rotational signal that is likely a result from potential escapers. The proper motion dispersion at large radii reported by Bianchini et al. ($3.5\pm 0.9\, \mathrm{km\, s^{-1}}$) has previously been attributed to dark matter. Here, we show that the LOS dispersion between 0.5 and 1 Jacobi radius is lower ($2.01\pm 0.18\, \mathrm{km\, s^{-1}}$), yet above the predictions from an N-body model of NGC 3201 that we ran for this study ($1.48\pm 0.14\, \mathrm{km\, s^{-1}}$). Based on the simulation, we find that potential escapers cannot fully explain the observed velocity dispersion. We also estimate the effect on the velocity dispersion of different amounts of stellar-mass black holes and unbound stars from the tidal tails with varying escape rates and find that these effects cannot explain the difference between the LOS dispersion and the N-body model. Given the recent discovery of tidal tail stars at large distances from the cluster, a dark matter halo is an unlikely explanation. We show that the effect of binary stars, which is not included in the N-body model, is important and can explain part of the difference in dispersion. We speculate that the remaining difference must be the result of effects not i