  In this note we discuss the (higher) regularity properties of the Signorini
problem for the homogeneous, isotropic Lam\'e system. Relying on an observation
by Schumann \cite{Schumann1}, we reduce the question of the solution's and the
free boundary regularity for the homogeneous, isotropic Lam\'e system to the
corresponding regularity properties of the obstacle problem for the
half-Laplacian.
