This is law enforcement just asking nicely for the video. They do this before getting a warrant because it is less work. If you don't comply, they'll just go to a judge and order Amazon to release it.
They should be universally told to pound sand without a warrant. You don’t give the armed representatives of the state everything they ask for just because they’re being polite; make them go through the proper procedures with oversight.
Probably when you know that your neighbor was burglarized or attacked, etc., you don’t want to impede the investigation. That’s worse than not taking care of your weeds or garbage in your yard in terms of getting along with neighbors.
“Don’t impede the investigation” is second only to “think of the children” for the erosion of our rights. Those who will abuse their powers will always have a great excuse for it, which is why we must be vigilant.
And of course the neighbor can freely hand over their own data to the cops if they want to; the cops should need a warrant to get that video from Amazon directly.