  In this paper, we discuss a rigidity property for holomorphic disks in
Teichm\"uller space. In fact, we give a refinement of Tanigawa's rigidity
theorem. We will also treat the rigidity property of holomorphic disks for
complex manifolds. We observe the rigidity property is valid for bounded
strictly pseudoconvex domains with $C^{2}$-boundaries, but the rigidity
property does not hold for product manifolds.
