  We consider circle patterns on closed tori equipped with complex projective
structures. There is an embedding of the space of circle patterns to the
Teichm\"{u}ller space of a punctured surface. Via the embedding, the
Weil-Petersson symplectic form is pulled back to the space of circle patterns.
We investigate its non-degeneracy. On the other hand, we also complete a
conjecture that the space of circle patterns is homeomorphic to the
Teichm\"{u}ller space of the closed torus.
