Let $X$ be a separable space and let $D(X)$ be the set of countable dense subsets of $X$. Consider an equivalence relation $\sim$, defined on $D(X)$, as follows: we say that $M \sim N$ if and only if there exists a homeomorphism $h: X \to X$ such that $h[M] = N$. Define the countable dense homogeneity degree of $X$ as the cardinality of the set of equivalence classes under the relation $\sim$. In this talk we discuss the countable dense homogeneity degree for local dendrites.