  Let $M$ be a complex surface. We show that there is a one-to-one
correspondence between torsion-free affine connections on $M$ and Riccati
distributions on $\mathbb{P}(TM)$. Furthermore, if $M$ is compact, then this
correspondence induces a one-to-one correspondence between affine structures on
$M$ and Riccati foliations on $\mathbb{P}(TM)$.
