Some Scottish advice, different laws, but the principles are the same.
The woman must approach the police first and make a complaint of assault and other crimes, beit threats or otherwise. If she has witnesses all the better, but that should not put her off recording the complaint. The police will do the rest.
Can I dispel this myth of 'pressing charges' - no-one presses charges aside from the prosecution service. Pressing charges is a 'The Bill' term and I hate it.
Should there be no further evidence to report a case , i.e. the neighbour is denying the assault, then the recording of this incident, will help build a picture for any future instances, and help to bring a case for prosecution.
If neighbour has any sense, he will take heed of any warning given and that will be that.