Legal Question in Landlord & Tenant Law in Maryland

All depends. If it was a dead tree that the property owner/manager negligently failed to remove, then the owner may well be responsible for any damage. If it was an otherwise healthy tree that fell from an Act of God (storm, lightening, etc.) then they may not be responsible, unless they failed to maintain a common area or otherwise breached some lease or other legal obligation. Insurance may provide coverage regardless of fault.

This answer offers general information and does not substitute for getting specific legal advice on the facts of your particular situation.