Okay, I find the above responses witty... so I must have been on this Forum for a while.
Dachshund, for your sanity, it is absolutely great that the police really did arrive and also that her husband spoke to you. I can truly sympathise, as I once had a really, really seriously mentally ill neighbour who caused a lot of trouble.
I suggest you document everything as, sadly, this is unlikely to be a once-off incident. As far as possible, get the names and addresses an direct phone numbers (and ideally email-addresses) of every police officer you speak to. If you don't have that of those who visited you, that's fine... it's a reason to go down to the Police Station to ask them, and to thank them for their intervention.
And of the husband.neighbour. And the other neighbours.
Then try to meet the husband-neighbour alone, or better still with your GF, if she lives with you at least some of the time.
He will probably be very grateful if you make it clear (as you have done in this thread) that though the incident upset and angered you, you do not, in fact, intend to press charges, as you understand that his wife is mentally ill.
Ask him for advice... what you should do if there is any further unpleasant incident.
Ask him for contact details: can you call him during the day and night, and on what number?
Ask him if you may have the telephone numbers (and ideally email addresses) of his wife's emergency contact persons, e.g. doctors, crisis centres, psychologists, nurses, parents, siblings or adult children, etc.
Once you've had that conversation, go down to the Police Station, and ask to talk to someone about when they came by to you. The purpose of that visit it twofold:
a) to demonstrate, by a calm demeanour, that you are a responsible citizen (and not the crazy one), and
b) to get them to write something about it in a file.
A police officer (not involved in the case) gave me the tip to do this.
He advised me to stay in the Police Station as long as possible, repeatedly expressing my concern about my neighbour's health, telling them that I want the situation to get better, and asking for their advice about how to proceed next time, if there is anything that causes me, or my other neighbours, upset, and thanking them for having spoken rationally to me and for helping to keep the trouble to a minimum. That officer said I should remain in the Station, talking, asking, expressing concern and gratitude, until I could get someone to actually make notes, a record, of my visit. And to ask for their card with the name of the person I spoke to.
Then to go to the neighbours, (the husband first, of course) and tell them you did that, and that Officer Mr X was very understanding and helpful, and them give them the contact details on the card, too.
Document all you have done, with date and time.
This tactic helps to ensure that there are not dozens of silly rumours, but to channel the information sensibly. And to make the file thicker.
Next incident, go through the same procedure again. If you can find a way to contact the doctors involved, do so. They are not allowed to discuss anything with you, of course, but they can receive information from you.
Once you have a few rounds of this, you can mail all the professionals (not the neighbours). Remember that they are not allowed to talk to one another, because of their professional data protection. Therefore, the therapist may not know at all that the police were involved, and the police may perhaps not even know that there is a doctor on the case, or of they do, who that doctor is. But you are outside of that, as long as you remain courteous and say nothing that is untrue.
The professionals are not allowed to reply to you with information about the woman and can, at most, simply say that they have received your mail (ask them to do that minimum). But in the case of my neighbour, it was only when I mailed all the professionals simultaneously, explaining the conversations I had had with each separate officer/therapist/social worker, etc., that they could each discover the missing parts of the puzzle. That opened the way, at last, for effective steps to be taken to find my neighbour better therapy (and, what a blessing, other housing) and only then did the situation de-escalate.
I wish you peace and wisdom!
P.S. just read your further post about the door. That's another of those things to document. And include in your circular mails. Who knows, the therapist may understand a deeper significance to this (e.g. a trigger/stimulus to remembering a trauma) and be able to bring the necessary persuasion to the landlord to fix the door.