First of all, don’t overreact, like the man in New Jersey who took out a gun and shot his neighbor’s drone out of the sky.
This sort of conduct will surely escalate tensions between you, and perhaps get you into deeper trouble with the police for criminal mischief.
Instead, act as you would act if your neighbor engaged in any other annoying conduct. Reach out by phone or email. Knock on the neighbor’s door. Ask politely to please refrain from flying the drone over your property—suggest that the neighbor fly it, perhaps, in a public park or simply hover it over his or her own backyard.
It’s possible that your neighbor did not realize that you noticed the little machine, or that it annoyed you. If there’s no fence between your properties, perhaps the neighbor didn’t even realize he or she was crossing the property line. The vast majority of neighbors will stop annoying conduct when asked nicely.
What if your neighbor does not respond to your emails, calls, or reasonable requests to fly the new toy elsewhere? You might have a cause of action in court known as private nuisance. The nuisance in this case, you could argue, is the noise of the drone—the whirring of the engine or blades—disrupting your quiet use and enjoyment of your premises. Filing a lawsuit will often prompt a neighbor to cease annoying conduct.
You could also make a legal case for trespass. The drone is flying over your property, outside the bounds of your neighbor’s yard. As mentioned above, you don’t necessarily own all of the air rights above your property. But you probably do own the immediate air rights surrounding the top of your home.
There is no unified answer to ‘how high’ homeowners own. Regulations vary by state. But any photographs that you take of the flying drone, to show a court how close the machine is getting to your yard or windows, would surely help convince a judge that the flight constitutes a trespass.