Rozansky-Witten theory is a 3d TQFT which is formulated in terms of a sigma model with a hyperk\"{a}hler target space. We focus on the case where the Hyperk\"{a}hler manifold is a K3 surface and analyze the corresponding TQFT with regard to a braided tensor category structure. To this end we formulate KZ-equations from which we extract the associator of the tensor category. This then leads to a representation of the braid group which we discuss.