A complementary tree dominating set of a graph G, is a set D of vertices of G such that D is a dominating set and the induced sub graph (V \ D) is a tree. The complementary tree domination number of a graph G, denoted by γctd(G), is the minimum cardinality of a complementary tree dominating set of G. An edge-vertex dominating set of a graph G is a set D of edges of G such that every vertex of G is incident with an edge of D or incident with an edge adjacent to an edge of D. The edge-vertex domination number of a graph, denoted by γev (G), is the minimum cardinality of an edge-vertex dominating set of G. We characterize trees for which γ(T) = γctd(T) and  γctd(T) = γev(T) + 1.