Is it permissible to inform the authorities about a family that has an annoying child during Ramadan?

Patience with a neighbor's harm carries a great reward. The Prophet, peace and blessings be upon him, mentioned that Allah loves a man who has a neighbor who harms him, and he endures his harm with patience. It is not part of good neighborliness to report the actions of a sick son to the authorities; rather, it is better to alleviate the burden on the family and be mindful of their situation, and to treat them as you would wish to be treated.