Using a modified bond fluctuation model, with only excluded-volume interactions, we demonstrate spontaneous curvature of 2D comb copolymer molecules, provided the side chains are allowed to flip from one side of the backbone to the other. When the side chains are not allowed to flip, the polymer conformations are very stiff. Once flipping is allowed, the polymers display a distinct curvature. We illustrate the curvature by presenting randomly selected snapshots. In addition, bond angle correlation analysis shows that in this case the polymer does not behave like a persistent wormlike chain. In connection to this we outline a model that incorporates curvature and is able to fit the correlation data. Further evidence for spontaneous curvature is given by scattering data displaying a pronounced peak that can be connected to conformational characteristics. Our findings are in good agreement with recent theoretical and experimental studies.