  The Schwarzschild-de Sitter solution in the Einstein theory with a positive
cosmological constant $\Lambda=m^2/\alpha$ becomes an exact solution to the
dRGT non-linear massive gravity theory with the mass parameter $m$ when the
theory parameters $\alpha$ and $\beta$ satisfy the relation $\beta=\alpha^2$.
We study the perturbative behaviour of this black hole solution in the
non-linear dRGT theory with $\beta=\alpha^2$. We find that the linear
perturbation equations become identical to those for the vacuum Einstein theory
when they are expressed in terms of the gauge-invariant variables. This implies
that this black hole is stable in the dRGT theory as far as the spacetime
structure is concerned in contrast to the case of the bi-Schwarzschild solution
in the bi-metric theory. However, we have also found a pathological feature
that the general solution to the perturbation equations contain a single
arbitrary function of spacetime coordinates. This implies a degeneracy of
dynamics in the St\"uckelberg field sector at the linear perturbation level in
this background. Physical significance of this degenercy depends on how the
St\"uckelberg fields couple observable fields.
