This would likely be determined in the contract between you and the client. You should consider the cost of litigation versus the amount of the fee you might recover. Unless this is an extremely expensive job, you would end up paying a lawyer far more to defend a lawsuit than the fee you might get if the client chooses to purchase the working file from you.
If you think this battle is worth fighting, contact a local attorney.
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Your understanding of industry practices doesn't mean anything.
The strength of your legal argument depends on copyright and contract law. So what's the language in your written contract - do you have one? Does it say you own the copyright to and proceeds of your work, and you only grant your paying client a license to use the final product? Federal copyright law says the creator of a product owns it, absent a "work for hire" contract shifting ownership to the employer. State contract law says that in most cases, the employer owns an employee's work.
As for the practical side of this, besides the cost of litigation which my colleague mentioned, your reputation and good will of this client is likely to greatly exceed the benefit of hanging on to these "working files." You get nothing but ill will from keeping them.
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This situation isn't so much about who will win a lawsuit, but how to avoid one.
It is easier and cheaper to just give them the files and be done with it.
I agree with my colleagues for the most part, but would probably not just hand over the working files (depending on how valuable the working files are to you). If the working files are something that you actually use for creating more than just this client's work, blindly handing over the files could cause issues if there is any litigation over copyright if you do end up using these files in preparing work for different clients.
I would recommend at least meeting with an intellectual property attorney and having the attorney read over the contract to see who does own the rights in the working files. If the attorney determines that you own the copyrights in the working files, you would likely be able to work out a settlement with the client that would be beneficial to both of you.
I do recognize that there is goodwill and reputation in dealing with the client, but you have already decided you do not work with this client. It is also better to have the client probably not want to hire you again than to hand over files that he could sell to others so they can complete the work themselves without having to hire you.
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You should look to your contract, not your "understanding" of industry practices. The contract, if any, governs not one party's "understanding" of what is in other deals.
The default is that you own the files if you are an independent contractor and the employer if you are an employee, but the contract may say otherwise.
The client likely has an implied license to use the files, so you will likely need to turn them over so they can be used. You should see an attorney so the license can be analyzed and the client's use can be limited as much as appropriate. However, that costs money and so you need to evaluate whether keeping these working files is really worth the cost of hiring an attorney to fight their attorney. Normally a consultation is worthwhile but not extended lawyer negotiations - unless this is really a very valuable set of working files. You should keep copies for your archival purposes, even if you do release the files, so you can prove what was released and what was not.
Your reputation is at stake here. These files are likely less important than the bad words this ex-client can spread about your firm. That is a call for you to make. You certainly would not give them any CAD programs, graphics programs and the like, but only the actual designs along with the names of any programs needed to access or edit them.
I am not your lawyer and you are not my client. Free advice here is without recourse and any reliance thereupon is at your sole risk. This is done without compensation as a free public service. I am licensed in IL, MO, TX and I am a Reg. Pat. Atty. so advice in any other jurisdiction is strictly general advice and should be confirmed with an attorney licensed in that jurisdiction.