You can negotiate anything you want with your neighbor, provided that the neighbor has not retained an attorney. In that case, the attorney will be your contact point. I would suggest calling animal control and asking what you have to do to get the dog back.
The best way to find out how you can get your dog back is to contact animal control right away to find out what procedures you need to undertake to try and get your dog back. There may be many requirements such as that the dog be spayed or neutered and that the dog be up to date on all its vaccinations. Animal control may also want to make sure your dog is not a danger to the community. It is also important to contact them right away so that they know that you want your dog back. Best of luck.
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