Assuming the intellectual property is worth something, its ownership should not be left to email exchanges.
While it is acceptable to give the CEO a heads up in an email that you would like to continue working on a product related to the idea you pursued together and to let him know that you would be willing to let him use the code you wrote in exchange for shared ownership rights in the other intellectual property of which the project consisted, his agreement to this should be documented with the help of an attorney.
Keep in mind that if you were not paid for your work and there were truly no agreements entered into by the parties, you don't have to hand over the code to the CEO. You can use this as leverage to come to an agreement about your respective intellectual property rights.
Best of luck!
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As correctly noted by Attorney Efimchik, this is not something to do via email. This requires resolution and reflection in a complete agreement. In short, this needs the involvement of an attorney.
Since you had no agreements and no entity at the outset, what you three had was a joint venture. This is much like a general partnership. Accordingly, an argument can be made that this asset is owned by the partnership and not any of the respective partners.
You should come to a license agreement that will work for all parties and include a clear termination of any claims between the former partners. Again, an attorney is needed for this and doing this by some form of email is a recipe for disaster and impending litigation.
Please hire a local attorney.
This answer is for informational purposes only and is not legal advice regarding your question and does not establish an attorney-client relationship.
The fact that you refer to someone as the CEO and yourself as CTO is interesting if there was no business entity. That being said, when intellectual property is created by more than one person without a written agreement or other clear understanding of the rights of the parties, the property is deemed to be co-authored, co-owned and considered a "joint work." In the case of a joint work, each author has the right to exploit the work as long as he/she provides the other author(s) with a fair share of the proceeds.
So, if you and the designer want to be deemed to own and control the work (and any improvements made to it), you need to meet with an intellectual property attorney in your area ASAP who can help you to come to an agreement with the CEO and then memorialize the rights of each party in the jointly developed technology.
Any answer or other information posted above is general in nature and is not intended, nor should it be construed, as legal advice. This posting does not create an attorney-client relationship between you and the posting attorney, and you are urged to engage a qualified attorney who is licensed to practice in the relevant jurisdiction.
You certainly need more than words for an e-mail. I cannot begin to advise you based on the information in your question, which is far too limited and unclear to generate meaningful legal advice,. For example, ordinarily, employees who work for a company and create inventions or original copyrighted works (such as software code) are deemed to have created "works for hire" belonging to the company. If you worked as an employee in this business, you may have no ownership rights in the software you developed. On the other hand, if this was a joint venture and you were one of the partners, you might have an ownership interest in the software (but you probably share that ownership interest with the CEO). Further, depending on the circumstances, you may owe a fiduciary obligation to the CEO, including the obligation to turn over the software to him. On the other hand, if there were no agreements or oral understandings governing your relationship, you may have no duty to turn over the code. You need to retain counsel to sort this out for you---the general advice you receive on this web-site is no substitute in a complex situation such as this for working with counsel.
Note that you should preserve all written communications, e-mails and text-messages relating to this matter---written communications like this can result in enforceable contracts, and these communications need to be analyzed carefully by your counsel to ascertain your rights and obligations.
Please don't e-mail him. This is a situation that requires at least a telephone conversation, better yet an in person meeting. You need to sit down with the CEO and determine whether you can reach an agreement for future use or "pivot" (?) before you release the code. You do not state whether you were paid (directly or with an interest in the project) so it is difficult to offer further direction. It appears that the "designer" is also ready to proceed with you. If this is true, it might be good to see if the 3 of you can reach a resolution other than with e-mails back and forth. There are simply too many unknown facts to give a solid direction, but start with a "let's resolve this" telephone call to see if the 3 of you can avoid the nastiness of a break up. If all are willing to meet, consult with a seasoned business attorney for settlement strategies.