Who is responsible for the damage of a trampoline when a pine tree fell on it?

[Tony Ngo]

Hello all,

A pine tree branch broke off and fell on the tenant trampoline in the back yard.  The tree belongs to the house.  It damaged the trampoline and the tenant is asking me to pay for a replacement.   I offered to pay for 1/2 of it.  I thought I was being nice by offering to help her with it.  She said it was my tree that damaged her trampoline and that I need to replace it.  Is this my responsibility?   

Thanks in advance for your inputs!