  B,V CCD frames have been used to derive surface brightness profiles for NGC
3201 out to ~18 arcmin. A total of 857 radial velocities with median precision
~1 km/s for 399 member giants have been used to trace the velocity dispersion
profile out to 32' (the approximate tidal radius from fits of single-mass,
isotropic King-Michie models to the cluster surface brightness profiles). The
median difference in radial velocity for stars on either side of an imaginary
axis moved through the cluster in 1 degree steps shows a significant maximum
amplitude of 1.22+/-0.25 km/s. We discuss possible explanations of this result,
including: (1) cluster rotation; (2) preferential stripping of stars on
prograde orbits near the limiting radius; (3) the projection of the cluster
space velocity onto the plane of the sky and (4) a slight drift in the velocity
zero point. It is difficult to identify the primary cause of the observed
velocity field structure unambiguously, and we suspect that all of the above
processes may play a role. The B,V surface brightness profiles and radial
velocities have been modeled with single- & multi-mass King-Michie models and
nonparametric techniques. The density and M/L profiles show good agreement over
1.5<R<10 pc, and both approaches suggest a steady rise in M/L with distance
from the cluster center. Due to the low cluster luminosity, we are unable to
place useful constraints on the anisotropy of the velocity dispersion profile,
though the global mass-to-light ratio is well-constrained by the models as ~2.0
+/-0.2 for the multi-mass and nonparametric models, compared to ~ 1.65 +/-0.15
for models having equal-mass stars. Our best-fit, multi-mass models have mass
function slopes of x~0.75 +/-0.25, consistent with findings that mass function
depends on the position relative to the potential of the Galaxy.
