Maybe. And if you do, there may be restrictions on what you can do.
No written documentation. We start with the principle that you, as the writer, own the copyright unless: (1) you signed a written assignment of the copyright to someone else; (2) you were employed to write the book (in which case the employer owns the copyright); or (3) you contracted to write the book, the work falls in one of the enumerated categories, and you signed a work made for hire agreement. Since there was no written documentation, we can probably eliminate (1) and (3).
Were you an employee? If the company can demonstrate that you meet the criteria of an employee (as set forth in this article), then you don't own the copyright. As you can see from a cursory look at the criteria, most writers in your situation are not employees.
Did others contribute to the writing? If the president (or someone else employed by the company) contributed materially to the creation of the book they would be joint authors with you and share the copyright. Alternatively, you and the president may have made separately copyrightable contributions to the book. We wrote about those situations in this article.
What if you claim copyright? If you claim copyright and reproduce the book, the company may object and advance the arguments above. They also may offer more creative arguments for example that you violated trade secrecy law (a long shot, unless you're considered an employee). Alternatively, they may claim that even if you own copyright, you created an implied license for the company to use, post, or publish the book on a nonexclusive basis. Such arguments have been successful in the past. If that argument were successful in your case, you would still own the copyright but you could not provide an exclusive license to a publisher (because the company would always have a right to reproduce the work as well).
