  We study reduced density matrices of the integrable critical RSOS model in a
particular topological sector containing the ground state. Similar as in the
spin-$1/2$ Heisenberg model it has been observed that correlation functions of
this model on short segments can be `factorized': they are completely
determined by a single nearest-neighbour two-point function $\omega$ and a set
of structure functions. While $\omega$ captures the dependence on the system
size and the state of the system the structure functions can be expressed in
terms of the possible operators on the segment, in the present case
representations of the Temperley-Lieb algebra $\text{TL}_n$, and are
independent of the model parameters. We present explicit results for the
function $\omega$ in the infinite system ground state of the model and compute
multi-point local height probabilities for up to four adjacent sites for the
RSOS model and the related three-point correlation functions of non-Abelian
$su(2)_k$ anyons.
