  We study the Euclidean two-point correlation function $G_q(x)$ of the
topological charge density in QCD. A general statement based on reflection
positivity tells us that $G_q(x)<0$ for $x\neq 0 $. On the other hand the
topological susceptibility $\chi_q=\int d^d x G_q(x)$ is a positive quantity.
This indicates that $G_q(x)$ developes a positive contact term at $x=0$, that
contributes to the determination of the physical value of $\chi_q$. We show
explicitly these features of $G_q(x)$ in a solvable nontrivial continuum model,
the two-dimensional $CP^{N-1}$ model in the large-N limit. A similar analysis
is done on the lattice.
