  We investigate the Ruppeiner geometry of the thermodynamic state space of a
general class of BTZ black holes. It is shown that the thermodynamic geometry
is flat for both the rotating BTZ and the BTZ Chern Simons black holes in the
canonical ensemble. We further investigate the inclusion of thermal
fluctuations to the canonical entropy of the BTZ Chern Simons black holes and
show that the leading logartithmic correction due to Carlip is reproduced. We
establish that the inclusion of thermal fluctuations induces a non zero scalar
curvature to the thermodynamic geometry.
