You don't have to clear it but at least keeping it to a level that it doesn't interfere with the view your neighbors paid for would be the responsible thing to do.
I deal with tree ordinances all of the time in my position.
1) A municipality's basic tree ordinances follow a template from ISA or copied from another municipality.
2) You are allowed to prune a neighbouring tree that is overhanging your property at the property line. Usually there is also a caveat enclosed that you can't perform any pruning that would be harmful to the tree or you can be sued for treatments, removal and/or replacement. Ordinance may also cover below ground abuse; root pruning, chemical applications, construction, etc.
3) A neighbouring tree that falls onto your house is considered an act of God UNLESS the tree had been inspected by an ISA certified arbourist and deemed hazardous. Or in the case of lightning strike or storm damage (uprooting) you have pointed out the hazard to the tree owner, documented with pics, contacted your ins. company who also made the tree's owner aware. In the event of lightning strikes; owners collect for damage to house and electronics, etc from ins. Usually have a rider for tree removal that is only $500. Leave hazard standing and then believe they can collect again, NOT. Neighbour makes ins. aware to CYO.
3a) Topping trees KILLS trees and makes them more hazardous.
4) Any ISA certified arbourist signed a code of ethics to maintain certification.
5) USVI doesn't have a tree ordinance.
Unfortunately, you're right.
We have no tree ordinances.
The rule of thumb here is that you can trim anything that overhangs your property.
I hate when I see a machete being used to trim or cut back branches and not big on pesticides use due to it harming everything else it comes in contact with and ends up running off into the sea.
Not to be controversial .....
I worked for a large electric utility in FL several years ago and the company's arborist suggested using concentrated Monsanto Roundup to permanently kill trees. He was particularly keen on using it clandestinely on neighbors' (or customers') trees that were not well maintained to force removal.
Not making this up. Couldn't if I tried.
I have seen that on YouTube. Requires drilling holes to poure Roundup