  In this paper, we characterize the boundedness, the compactness and the
Hilbert-Schmidt property for composition operators acting from a de
Branges-Rovnyak space $\mathcal H(b)$ into itself, when $b$ is a rational
function in the closed unit ball of $H^\infty$ (but not a finite Blaschke
product). In particular, we extend some of the results obtained by D. Sarason
and J.N. Silva in the context of local Dirichlet spaces.
