How liable are you if you sell/give away a puppy or even an adult dog, and the animal bites or mauls someone?
Does the amount of time between the exchange and the attack matter? If someone sells an adult dog and 3 years later he bites his new owner is the liability different than if he bites after 3 days?
Is there any case law on this subject?
You probably could be held responsible for hiding known cases of dog bites or attacks. You shouldn’t do that if you are giving away a dog under any circumstances. If you didn’t know about any aggressive behavior by the dog, it wouldn’t seem reasonable to hold you responsible.
Speaking in generalities here:
In order to be liable you have to breach some duty. In the case of a dog transfer, that could be something like failing to tell the new owner if the dog had ever bitten anyone in the past. If you had no such knowledge, there would be no breach of duty.
State laws, of course, will vary. I found this link of Wisconsin Dog laws (I assumed Wisconsin based on your location)
I know about this statute, but I can’t find the answer I’m looking for. The liability issue seems to be aimed at the current owner, and as for sellers it only addresses licensed sellers.
Say I’m 75 years old and moving into a rest home and can’t keep my 5 year old dog any more. I give him to my neighbor (she gets a city dog license in her name) and 2 weeks later he bites her. He’s never bitten anyone before. Am I liable?
Unless there is some weird statute in force, I can’t imagine any theory under which you would be.
My suggestion would be to nuke the dog from orbit. It’s the only way to be sure. 
Now see this is where me and you differ. If I was a dog and you gave me away, I wouldn’t bite OTHER people. I’d bite YOU 
I don’t have a specific reference, but there are ‘rescue’ organizations that can handle the transfer of a dog to a new owner for you, even one you select. They can probably answer all the questions for your locality, and may be able to protect you from liability, but it doesn’t sound like their would be any. I hope you can still see your dog occasionally after you move, you’ll both really appreciate it.
Write up a legal document that you & her both sign. Include in that transfer of ownership to her in return for some consideration (like $1), arrangements for visitation, assertion by you that the dog is, to the best of your knowledge, in good health, AND from her a release from all liability for future actions of the dog.
Print it up real fancy and ceremoniously sign it and present it to her. She’ll be flattered at how you are officially making her the owner, and probably won’t notice the release from liability in it. (Though legally, you might be better if it was clearly discussed with her.)