Summary: A Connection Matrix Theory approach is presented for Morse-Bott flows \(\varphi\) on smooth closed \(n\)-manifolds by characterizing the set of connection matrices in terms of Morse-Smale perturbations. Further results are obtained on the effect on the set of connection matrices \(\mathcal{CM}(S)\) caused by changes in the partial orderings and in the Morse decompositions of an isolated invariant set \(S\).