We study the edge overlap and local limit of the random spanning tree in random environment (RSTRE) on the complete graph with $n$ vertices and weights given by $\exp(-βω_e)$ for $ω_e$ uniformly distributed on $[0,1]$. We show that for $β$ growing with $β= o(n/\log n)$, the edge overlap is $(1+o(1)) β$, while for $β$ much larger than $n \log^2 n$, the edge overlap is $(1-o(1))n$. Furthermore, there is a transition of the local limit around $β= n$. When $β= o(n/ \log n)$ the RSTRE locally converges to the same limit as the uniform spanning tree, whereas for $β$ larger than $n \log^λn$, where $λ= λ(n) \rightarrow \infty$ arbitrarily slowly, the local limit of the RSTRE is the same as that of the minimum spanning tree.