  Let $T$ be a tree with vertex set $\{1, \ldots, n\}$ such that each edge is
assigned a nonzero weight. The squared distance matrix of $T,$ denoted by
$\Delta,$ is the $n \times n$ matrix with $(i,j)$-element $d(i,j)^2,$ where
$d(i,j)$ is the sum of the weights of the edges on the $(ij)$-path. We obtain a
formula for the determinant of $\Delta.$ A formula for $\Delta^{-1}$ is also
obtained, under certain conditions. The results generalize known formulas for
the unweighted case.
