  An edge-colored multigraph $G$ is rainbow connected if every pair of vertices
is joined by at least one rainbow path, i.e., a path where no two edges are of
the same color.
  In the context of multilayered networks we introduce the notion of
multilayered random geometric graphs, from $h\ge 2$ independent random
geometric graphs $G(n,r)$ on the unit square. We define an edge-coloring by
coloring the edges according to the copy of $G(n,r)$ they belong to and study
the rainbow connectivity of the resulting edge-colored multigraph. We show that
$r(n)=\left(\frac{\log n}{n}\right)^{\frac{h-1}{2h}}$ is a threshold of the
radius for the property of being rainbow connected. This complements the known
analogous results for the multilayerd graphs defined on the Erd\H{o}s-R\' enyi
random model.
