Dispute with Neighbour over a coconut tree

We have one coconut tree well within our compound since almost last 40 years and we have been in this property since last 11 years. Our neighbor is also there in the property since last 40 years. They did not complain in these 40 years about the falling coconuts and leaves, but suddenly since last one year they creating issues and asking us to do a permanent solution to falling coconut and leaves. The tree is well within our compound and leaning to our home and till now with falling coconut neighbor has not faced any damages. Now they have also involved local police and municipality. we have provided our response to both Police and municipality and awaiting reply. We agreed that we will remove coconuts time to time from tree, but they are not agreeing to it. Want to know our legal stand on this. Can we take this case further in court of law and is this a civil case or criminal case and can Police get involve in this. Please help with your expertise. Thanks, Mangalore, Karnataka