Most people who only have liability, or the bare minimum, are not covered for damage to their car. Your liability insurance only covers damage you cause to someone else's property.
If your car is damaged in a storm or hurricane, or if there are winds that knock a tree branch onto your car, your liability policy will not cover that.
What you need is comprehensive auto insurance. Comprehensive auto insurance will cover things such as wind damage, storm damage, flooding, hurricanes, damage caused by animals and theft. Yes it costs more. Is it worth it? That's up to your. It really depends on your finances and the type of car you drive.
So, to simplify it once again:
- Liability coverage: Mandatory in all states, only covers damage you cause with your car to someone else's property.
- Comprehensive Auto Insurance: Voluntary coverage that covers damage to YOUR car caused by "Acts of God", theft, animals, etc.