There are many problems that lead to trees becoming dangerous in a storm. Branches can have double leaders, making them susceptible to weakness. There can be subtle signs of rot in a tree's trunk, leading to structural weakness. An overgrown branch may look healthy, but be too close to a power-line or structure, posing another risk. And then there can be issues that have resulted from bad tree lopping practices in the past. Tree weaknesses often come as a result of unskillful lopping or topping.
For these reasons, and many more, you should not perform your own tree work on potentially dangerous trees. You should enlist the services of a qualified arborist. Have the overhanging branches trimmed and pruned. Have large or compromised trees removed...preferably before the storm season begins. This will help you to minimise dangers ahead of time.