Take my neighbor to civil court over dead tree?

[Jordan Sachs]

A dead tree from the property next door fell on the garage of one of my properties. I understand this is my responsibility and I filed an insurance claim and the garage is currently being rebuilt as the entire thing was destroyed. However, my contractor has informed me that a large part of the dead tree is still hanging over the garage and is likely going to fall during another storm and probably destroy the garage again. I was told I can pay $3k to remove the part of the tree that's hanging over the garage (in addition to the $3k deductible I'm already paying) or I can take the next door neighbor to civil court because the tree over the garage is actually dangerous to the tenant who lives there. 

Does anyone have any idea if this would be worth going to court over and if it is and I get the judgement I want is it enforceable? The house is in Allentown, PA. Any info/input would be greatly appreciated. Thanks in advance!