We present SplineDist, an instance segmentation convolutional neural network for bioimages extending the popular StarDist method. While StarDist describes objects as starconvex polygons, SplineDist uses a more flexible and general representation by modelling objects as planar parametric spline curves. Based on a new loss formulation that exploits the properties of spline constructions, we can incorporate our new object model in StarDist's architecture with minimal changes. We demonstrate in synthetic and real images that SplineDist produces segmentation outlines of equal quality than StarDist with smaller network size and accurately captures non-star-convex objects that cannot be segmented with StarDist.