Tree roots to adjoining property

[Chirag Patel]

Hi, 

I recently purchased a rental property which had been on the market for some time now, 

As soon a tenant moved in, my neighbor said they wanted to rebuild the fence, and are asking me to remove a tree which is in between both properties (trunk is on my side) 

The roots are growing above ground on their end, and my neighbor is asking me remove it (will definitely cost a decent amount.) I suggested to build the fence a foot or so in their property(they do not want to do this)  or cut our the root portion from the bottom of the fence(also do not want to do this)

My property is in Woodrbidge, NJ, 

Does anyone have any advice for me? Do I have to remove it? Am I liable?