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I do not know if anyone can ever be fully free from liability when trampolines are involved. Let me share a true story with you.
A family had a very nice folding trampoline that they would open up when they were using it. When not in use it was folded and locked with a chain and stored in the garage.
One day a couple of guys who were drunk and knew about the trampoline went into the garage, cut the chain on the tramp, set it up, and began jumping on it while the homeowners were gone. One of the guys fell off and broke a bone.
The worst part of the story is that the guy sued and won despite all of the precautions that the family took. The charge was willfully allowing a potential hazard to exist or something like that.
Yeah, makes me sick too. Mad even.
This family did not have waivers or signs or anything but still...
Anyway, I am not a lawyer but I would ask these questions from what you have given...
1. Does the landlord know that the tramp is in the yard?
2. If yes, does the landlord's insurance company know that it is there?
3. Is the fence REALLY going to stop someone from jumping on it anyway? Outsiders, other tenants of the property, or the friends of other tenants?
I think that waivers and signs are a great idea but I do not think that they will prevent someone from getting sued. I think it would help the case to have them though.
As far as who is liable... again, I am not a lawyer but my opinions would be...
1. Since your daughter is of legal age and it is her trampoline, you would most likely not have any liability. Your daughter and the property owners would share some liability. Woe the landowner if the insurance company doesn't know about the tramp.
2. Waivers are great but I would be concerned about the stray human that chooses to jump and has never signed anything.
3. Perhaps her friends might not sue her. What about the parents of those friends? Lawsuits can come from some strange places at times.
4. Will waivers and signs prevent lawsuits? NO
5. Will waivers and signs prevent you from losing a lawsuit? NO
6. I do think that waivers and signs, however, will help your chances of winning.
7. Contact a local lawyer for more specific, legal, information.
8. Negligence can be avoided MOST OF THE TIME when it can be proven that you have acted in a manner that a reasonable and prudent person would. Obviously, the story I gave was more of an exception than the rule but I want you to understand that I don't think we are ever 100% safe from liability. The plaintiff might just have a super awesome lawyer on their side to find the loopholes and such.
Good luck and stay safe!