  We prove up-to-constants bounds on the two-point function (i.e.,
point-to-point connection probabilities) for critical long-range percolation on
the $d$-dimensional hierarchical lattice. More precisely, we prove that if we
connect each pair of points $x$ and $y$ by an edge with probability
$1-\exp(-\beta\|x-y\|^{-d-\alpha})$, where $0<\alpha<d$ is fixed and $\beta\geq
0$ is a parameter, then the critical two-point function satisfies \[
\mathbb{P}_{\beta_c}(x\leftrightarrow y) \asymp \|x-y\|^{-d+\alpha} \] for
every pair of distinct points $x$ and $y$. We deduce in particular that the
model has mean-field critical behaviour when $\alpha<d/3$ and does not have
mean-field critical behaviour when $\alpha>d/3$.
