  Given a graph $G$, a subset of vertices is called a maximum independent set
if no two of the vertices are adjacent and the subset has maximum cardinality.
The independence number $\alpha(G)$ of $G$ is the cardinality of a maximum
independent set. A subset of vertices is called a maximum dissociation set if
it induces a subgraph with vertex degree at most 1 and the subset has maximum
cardinality. The dissociation number $\psi(G)$ of $G$ is the cardinality of a
maximum dissociation set. Alvarado et al. [Discrete Math. 342 (2019) 934--942]
proved that a tree $T$ of independence number $\alpha$ has at most
$2^{\alpha-1}+1$ maximum independent sets. In this paper, we consider the
corresponding problem for dissociation sets and show that the number of maximum
dissociation sets in a tree of dissociation number $\psi$ is at most
\begin{center} $\left\{
  \begin{array}{ll}
  1,& \hbox{if $\psi=1$;}
  3^{\tfrac{\psi-1}{2}-1}+1,& \hbox{if $\psi$ is odd and $\psi>1$.}
  3^{\tfrac{\psi}{2}-1}+\tfrac{\psi}{2}+1,& \hbox{if $\psi$ is even.}
  \end{array} \right.$ \end{center} We also characterize those trees achieving
this maximum value.
