Let \(G=(V,E)\) be an arbitrary graph, and \(d_ i>0\) be the degree of the vertex \(v_ i\in V\). D(G) denotes the diagonal matrix whose (i,i)-entry is \(d_ i\), and A(G) denotes the adjacency matrix of the graph G. The matrix \(L(G)=D(G)-A(G)\) will be called the Laplacian matrix of the graph G. Brualdi and the author have obtained bounds for PerL(G) where PerL(G) is the permanent of the matrix L(G) and G is a bipartite graph. They have also introduced the notion of the Laplacian ratio \(\pi (G)=PerL(G)/d_ 1d_ 2\cdot \cdot \cdot d_ n\) and obtained a lower bound for \(\pi\) (G) where G is a bipartite graph. In this work upper and lower bounds are obtained for \(\pi\) (T), namely \(\pi (T)\geq \pi (C_ k)\) and \(\pi\) (T)\(\leq 2\) k, where T is a tree, k is the maximal number of independent edges of T, and \(C_ k\) is the tree obtained by adjoining a pendant edge to each vertex of the path \(P_ k\).