Tree branches extending into nieghbors property

[Scott Rohweder]

My tenants mentioned to me that the neighbor behind my rental property has been complaining about the branches from a very large tree on my property extending over into their yard blocking the sunlight to their garden.  They are asking that I hire a company to trim the branches back to the property line.  If the branches are not causing any damage or potential damage to my neighbors property, is that my responsibility/cost to remedy? 

Thanks