Hello and welcome to JustAnswer. Please note: This is general information for educational purposes only and is not legal advice. No specific course of action is proposed herein, and no attorney-client relationship or privilege is formed by speaking to an expert on this site. By continuing, you confirm that you understand and agree to these terms.
I am sorry to hear about this situation. The authorities have to respond to any (credible) call because this is a departmental requirement. I am afraid that they cannot be sued under such circumstances.
And, no person can be restricted from contacting emergency services. However, what someone in your situation can do is threaten to sue them civilly, or do so.
To sue in a state court, one needs to have a "cause of action." There are numerous causes of action, such as "breach of contract," "negligence," "fraud," "unjust enrichment," etc., as well as causes of action rooted in statutory law. Every state has their own although they are very similar to each other in every state because they all stem from the same common law. A pleading in Court needs at least one cause of action, although it is not unusual to have more than one.
Their actions arguably give rise to defamation and intentional infliction of emotional distress.
The elements of defamation in Missouri are: 1) publication, 2) of a defamatory statement, 3) that identifies the plaintiff, 4) that is false, 5) that is published with the requisite degree of fault, and 6) damages the plaintiff's reputation. Nazeri v. Missouri Valley College, 860 S.W.2d 303 (Mo. banc 1993).
Intentional infliction of emotional distress is when (1) the defendant acts intentionally or recklessly; (2) the defendant's conduct must be extreme or outrageous; and (3) the conduct must be the cause (4) of extreme emotional distress. Boes v. Deschu, 768 S.W.2d 205, 207 (Mo.App. 1989).
Someone in your situation can threaten a lawsuit and punitive damages in judgment unless the the neighbor does not cease/desist. That normally works. Using an attorney for the letter is best.
Please note: If I tell you simply what you wish to hear, this would be unfair to you. I need to be honest with you and sometimes this means providing information that is not optimal. Negative ratings are reserved for experts who are rude or for erroneous information. Please rate me on the quality of my information; do not punish me for my honesty.
I hope this helps and clarifies. Please use the SEND or REPLY button to keep chatting, or please RATE when finished. You may always ask follow ups at no charge after rating. Kindly rate my answer as one of TOP THREE FACES/STARS and then SUBMIT, as this is how experts get credit for our time. Rating my answer the bottom two faces/stars (or failing to submit the rating) does not give me credit and reflects poorly on me, even if my answer is correct. I work very hard to formulate an informative and honest answer for you; please reciprocate my good faith with a positive rating.