A firearm was shot at the window of a house while a mother slept with her two young children, aged one and three years old.
The bullet went through the upstairs window of the house in Church Crookham, near Fleet in Hampshire, at 2340 BST on Friday. but nobody was injured.
Police said a motive had not yet been established and a "random discharge cannot be discounted".
They closed off Aldershot Road while they carried out forensic searches on Saturday.
House-to-house inquiries have also been carried out.
They are appealing to anyone who knows anything about the incident to contact officers involved in Operation Almeda.