Check if a book is in the public domain? asks how one can research whether a book has fallen in the public domain. Is there a way to go one step further, to protect oneself, either getting some official guarantee that it is not in the public domain that can be used in a courtroom, some official list (e.g. maybe a law university keeps a list which would be legally recognized), or perhaps insurance?
The closest that you can come to an official list is the registry maintained by the US copyright office. That tells you which copyrights have been registered, and does not tell you much about items not on the list. But, if a work is registered (and the copyright has not expired, which you can calculate), you know it is not in the public domain. The question is a bit odd, because I don't see how you could ever need to prove legally that a random work is not in the public domain.
Copyright is inherent in the act of creating a work and requires no additional actions, under current law. If you know the date of creation of the work, you can figure out whether the work is old enough that its copyright has expired. If you know that the work is "prepared by an officer or employee of the United States Government as part of that person’s official duties", you know that it never was protected. These are the main sources of "being in the public domain" under US law, but the law doesn't actually talk about "public domain", it says when things are or are not protected by copyright.
A third source for being "in the public domain" is a "public domain" license, there an author says something sounding like "anybody can use this work as they see fit". CC0 is one attempt to emulate the concept of "public domain", by waiving rights and granting permission. Still, the work is protected by copyright if not in one of the two actual public domain categories. Also, under 17 USC 203 such a license can be terminated under certain conditions (during a period between 35 to 40 years after creating the work, approximately).