  The 2-dimensional BF theory is both a gauge theory and a topological Poisson
$\sigma$-model corresponding to a linear Poisson bracket. In \cite{To1},
Torossian discovered a connection which governs correlation functions of the BF
theory with sources for the $B$-field. This connection is flat, and it is a
close relative of the KZ connection in the WZW model. In this paper, we show
that flatness of the Torossian connection follows from (properly regularized)
quantum equations of motion of the BF theory.
