The concept of complementary tree vertex edge dominating set (\emph{ctved}-set) of a finite, connected graph $G$ is introduced and characterization result for a non empty proper subset of the vertex set $V$ of $G$ to be a \emph{ctved}-set is obtained. The minimum cardinality of a \emph{ctved}-set is denoted by $\gamma ctve(G)$ and is called as \emph{ctved} number of $G$. Bounds for this parameter as well, are obtained. Further, the graphs of order $n$ for which the \emph{ctved} numbers are $1,2,n-1$ are characterized. Trees having \emph{ctved-numbers} $n-2$, $n-3$ are also characterized. Exact values of this parameter for some standard graphs are given.