There are two questions here.
1. Did you do anything wrong? No. You gave 60 days notice, which hopefully fully meets the terms of your contract. You gave it to the responsible program director, to whom you report. If this is consistent with the notice required in your contract, then you are on solid ground.
2. Did you in any way commit unprofessional behavior by resigning through your boss? No. Did you not follow a paperwork procedure? Possibly, but this does not rise to the level of unprofessional behavior. If you gave proper notice to your program, and they were aware of your intentions, you should be on solid ground. You may wish to discuss this with an attorney who is experienced in licensing matters in both states.
This is likely not to be a problem at all. Most state apps will ask a question like, "Have you ever been terminated from a residency, or resigned under the threat of termination?"
You did not. You gave the program director 60 days notice. If you did sign the "mutual termination form," that was the mistake. But, assuming you have a letter or other evidence you gave the PD adequate notice, you should be fine, and even absent that, any explanation required by the board should rapidly put this to rest. I doubt an institution, if called on it, would be able to justify this charge, outside of your signature on the form.
The moral of this story is don't sign something just because someone says you have to, especially if you don't agree with what you are signing. For those who might be facing this situation in the future, Always ask yourself the following questions:
1. If I do not sign this form, what are the consequences of not signing it?
Can the institution with-hold something I need or otherwise hurt me?
Will signing a form with adverse and incorrect information hurt me more?
If in doubt, tell the folks you need a couple days to study the matter. You'll be in touch.
Then check with a qualified attorney.
2. If do sign the form, how will it help me in the future?
If you disagree with information on the form, or there is information on the form that is untruthful, incorrect, or otherwise wrong, then cross it out, amend it, or otherwise make it say what you want to say. Then initial it and date it. Remember, the folks that want you to sign this form are not necessarily your friends, and also remember anything you say or write is evidence, and might be used against you. If they don't like you amending the form, they will say so, they will badger you, but there's very little they can do to force you to sign anything against your will.
Normally, a program that you are switching to requires a letter from the old program, and your present program should be able to produce that.
These days, the phrase "unprofessional behavior" can mean nearly anything from not brushing your teeth to really awful things. There was no unprofessional behavior here, and the fact that you've completed another residency should attest to that.
The states will want you to answer their questions truthfully and directly, and without deceit. If your state asks a specific question then answer it, directly. If they do not, then complete the application.
