Generally speaking, park owners are liable for property damage and bodily injury caused by trees if the tree or limb was dead or dying when it fell. Therefore, dead or dying trees and limbs should regularly be removed from your property. Due to the high hazard of tree trimming, we recommend that you hire contractors to do that for you. If you have maintenance people and your workers compensation insurance company learns your workers trim trees, they'll likely non-renew your insurance.
Tree damaged caused by healthy trees that fall over generally won't result in your ultimate liability, but that doesn't mean that some tenant won't demand you compensate them when a wind storm blows over a healthy tree and it badly damages their home. Large trees can fall right through any home.