If the neighbors tree has limbs or branches overhanging your property then yes you can have those tree branches or tree limbs cut.
There's nothing illegal about cutting tree limbs or tree branches that overhang onto your property.
I would first discuss it with the neighbor and then if they do not want you cutting it then tough luck and if they cause issues then just call the cops.
I've cut tree limbs that overhung onto my roof from the neighbors tree and never had any problems but there could be that one problem neighbor.
I would just get it cut or cut it and then if there's any issues call the police because the limbs or tree branches are encroaching your property.