Trim your tree branches if there's any way they may hit roofs if the wind blows or gusts high enough.
When Ike was about to hit us, my neighbor and I found ourselves inspecting things outiside at the same time. He had a two-story home and a tall tree with branches dangerously close to his roof for the storm we were expecting.
There wasn't a tall-enough ladder close enough for him to get to it. I offhandedly said, well if worse comes to worse insurance will pay. He response was I have an $8,000 deductible.
So, I suggest you not wait too long if your branches might be an issue for you or your neighbors. Much less expensive to trim