Where a digital file of a book, a scan of a book, and a physical copy of a book are usually all considered equivocal copies by Copyright law, the same cannot always be said in the world of 3D printing. Copyright may protect the design of a 3D object, the file that the printer and program use to create the object, and the final object in different ways.
Are you beginning with a scan of a pre-existing object?
Are you beginning with a design file created by someone else?
Are you intending to sell or license your 3D projects?
Your answers to these questions will help you determine whether you need to request permissions from the copyright owner and define what rights you will have as the creator of your 3D printed work.
These are articles and informative sites that explore how copyright applies to 3D printed objects and the process of 3D printing.