We propose a framework for performing CAD-compatible topological optimization of Kirchhoff-Love (KL) shells under the isogeometrical paradigm [3]. A multi-patch non-conforming optimization domain is described as a collection of NURBS surfaces. The material distribution within these surfaces is optimized by using the Level Set Method for compliance and volume minimization [1,2]. The descent direction of the cost function is obtained with an expression for the shape derivative accounting for the separation of membrane and bending strains on the KL model. As the evolving shapes are implicitly defined by a NURBS level set function (LSF), our method can manipulate CAD-compatible geometries throughout the optimization process. The LSF allows for the precise delineation of the domain boundaries, which enables seamless export of the optimal designs to CAD/CAM software for manufacturing. In addition, we demonstrate the strong compatibility of the method with real-world engineering applications by also handling complex non-conforming multi-patch geometries. The approach is tested on a series of numerical examples, featuring three-dimensional non-conforming shells, which are available in an open github repository. This implementation adds a topology optimization layer to the fenics-based library PENGoLINS [4].