If the woman is making repeated phone calls and complaints after being asked to cease and desist, and those complaints are false, the other neighbors can sue her in civil court on the grounds of intentional infliction of emotional distress and slander/defamation of character.

Here is the relevant statute from the California Civil Code:

44. Defamation is effected by either of the following:
(a) Libel.
(b) Slander.



45. Libel is a false and unprivileged publication by writing,
printing, picture, effigy, or other fixed representation to the eye,
which exposes any person to hatred, contempt, ridicule, or obloquy,
or which causes him to be shunned or avoided, or which has a tendency
to injure him in his occupation.



45a. A libel which is defamatory of the plaintiff without the
necessity of explanatory matter, such as an inducement, innuendo or
other extrinsic fact, is said to be a libel on its face. Defamatory
language not libelous on its face is not actionable unless the
plaintiff alleges and proves that he has suffered special damage as a
proximate result thereof. Special damage is defined in Section 48a
of this code.



46. Slander is a false and unprivileged publication, orally
uttered, and also communications by radio or any mechanical or other
means which:
1. Charges any person with crime, or with having been indicted,
convicted, or punished for crime;
2. Imputes in him the present existence of an infectious,
contagious, or loathsome disease;
3. Tends directly to injure him in respect to his office,
profession, trade or business, either by imputing to him general
disqualification in those respects which the office or other
occupation peculiarly requires, or by imputing something with
reference to his office, profession, trade, or business that has a
natural tendency to lessen its profits;
4. Imputes to him impotence or a want of chastity; or
5. Which, by natural consequence, causes actual damage.