  A set $D$ of vertices of a graph $G$ is a total dominating set if every
vertex of $G$ is adjacent to at least one vertex of $D$. The total domination
number of $G$ is the minimum cardinality of any total dominating set of $G$ and
is denoted by $\gamma_t(G)$. The total dominating set $D$ is called a total
co-independent dominating set if $V(G)\setminus D$ is an independent set and
has at least one vertex. The minimum cardinality of any total co-independent
dominating set is denoted by $\gamma_{t,coi}(G)$. In this paper, we show that,
for any tree $T$ of order $n$ and diameter at least three, $n-\beta(T)\leq
\gamma_{t,coi}(T)\leq n-|L(T)|$ where $\beta(T)$ is the maximum cardinality of
any independent set and $L(T)$ is the set of leaves of $T$. We also
characterize the families of trees attaining the extremal bounds above and show
that the differences between the value of $\gamma_{t,coi}(T)$ and these bounds
can be arbitrarily large for some classes of trees.
