  We analyze the $\delta=2$ Tomimatsu-Sato spacetime in the context of the
proposed Kerr/CFT correspondence. This 4-dimensional vacuum spacetime is
asymptotically flat and has a well-defined ADM mass and angular momentum, but
also involves several exotic features including a naked ring singularity, and
two disjoint Killing horizons separated by a region with closed timelike curves
and a rod-like conical singularity. We demonstrate that the near horizon
geometry belongs to a general class of Ricci-flat metrics with
$SL(2,\mathbb{R})\times U(1)$ symmetry that includes both the extremal Kerr and
extremal Kerr-bolt geometries. We calculate the central charge and temperature
for the CFT dual to this spacetime and confirm the Cardy formula reproduces the
Bekenstein-Hawking entropy. We find that all of the basic parameters of the
dual CFT are most naturally expressed in terms of charges defined intrinsically
on the horizon, which are distinct from the ADM charges in this geometry.
