A 3D scan can be lots of work. In fact, it can be so much work that you think of doing it for others as a type of contract work. At the same time, you want to display your previous models to, say, find new scanning jobs. Here is where some legal difficulty starts.
First, it is save to assume that the vast majority of 3D objects you are going to create will be replicas of existing objects and thus not be covered under copyright.
Second, it is also save to assume that this situation is not going to change in the near future. Every new technology has enjoyed a few years of legal negligence before it was regulated. Whether this regulation was for the better is another story. But for now it is enough to look at the situation for 2D replicas of works of art to understand that the copyright situation most likely will to be of little relevance for 3D scanning and models. (Weinberg 16)
But image you were contracted by X to produce a 3D scan of a unique object. One the one hand, you want to make sure your work is only used in a way both parties agreed to. So far, the words agreed to and contracted make it clear that a contract is the form of choice to assure control over the terms and conditions of the labor exchange that is about to happen. How effective that contract will be depends on your exact knowledge of the legal situation, while the amount of control most likely correlates with your ability to pay for a long-winded legal battle over ownership of the 3D object.
But that was the easy part. Now let us image you wanted to present and share your creations with the world. Maybe you hope someone will help you, teach you a new technology or just comment on your work. Maybe you also think people should be able to print your creation of they want, but you definitely do not think it should be sold on for money – especially without your name on it. You could of course enter a contract with every one of those people, yet image a place like scetchfab.com where you have to contact and negotiate a contract with every member.
What fills the gap between contract and copyright could be a good license. This model has been successfully used in software development and can easily be adapted for 3D models. A license to some extend avoids the hazardous definitions needed for the copyright debate and provides a simple and easy-to-use base for distribution of material. So to make your work known to the public, you might want to use something like a Creative Commons Attribution NonCommercial (CC-BY-NC) license.
This short text is meant to make people think about if and how they want to publish their 3D scans and models. The earlier makers begin to employ a good licensing practice, the better. The scene is still in its infancy and we are seeing a lot of creativity and work invested in 3D scanning and printing. Eventually, this is going to change towards a more professionalized, closed sphere and at some point we will see a large-scale capitalization of printing knowledge and printed products. Everyone who is currently experimenting should be aware of this and take small but important steps towards retaining some control over their own work. Try https://tldrlegal.com/ as a starting point.