  Rozansky and Witten proposed a 3-dimensional sigma-model whose target space
is a hyperk\"ahler manifold. They conjectured that this theory has an
associated TQFT, with Hilbert spaces given by certain cohomology groups of the
hyperk\"ahler manifold. On the other hand, there is a certain modified TQFT
constructed by Murakami and Ohtsuki using the universal quantum invariant. We
explain how the Rozansky-Witten TQFT can be obtained from the latter by
applying a `hyperk\"ahler weight system'.
