Neighbor wants me to remove tree with branches falling in her yard

[Jon W.]

Hello BP,

I have a rental property with a lot of large trees.  On one side, some of these trees are hanging lower and drops small branches into the neighbors yard.  She has been complaining about the constant cleanup of these small branches and wants me to either remove the trees or cut them back.  I live in Michigan and do not know my liability.  The trees provide a lot of shade to my yard and her yard.  Paying money to cut back perfectly healthy trees seems like a waste.

Has anyone come across this issue with a neighbor and what would be the best course of action. 

I am leaning toward paying a company to cut the trees back to avoid any more conflict.

Thanks,

Jon