  We classify the sign of the critical Casimir force between two finite objects
separated by a large distance in the two dimensional systems that can be
described by conformal field theory (CFT). In particular, we show that as far
as the smallest scaling dimension present in the spectrum of the system is
smaller than one, the sign of the force is independent of the shape of the
objects and can be determined by the elements of the modular $S$-matrix of the
CFT. The provided formula for the sign of the force indicates that the force is
always attractive for equal boundary conditions independent of the shape of the
objects. However, different boundary conditions can lead to attractive or
repulsive forces. Using the derived formula, we prove the known results
regarding the Ising model and the free bosons. As new examples, we give
detailed results regarding the Q=3-states Potts model and the compactified
bosons. In particular, for the latter model we show that Dirichlet boundary
condition does not always lead to an attractive force.
