Be Careful With Your Tone:
It depends on if the person knows the things to be false or not. A lot of people will file things in court in an effort to intimidate you into settling an issue in their favor. Taking you to court and testifying that something they know is false is true is perjury. Saying something is true when you know it to be false is just lying anywhere else. 'Saying falsehoods' implies lying but doesn't say it as aggressively.
Saying someone is wrong is a whole different thing. If someone is crazy, then they could be hallucinating, delusional, or paranoid. Avoid saying that unless you really believe they are. Mostly, I'd go with just plain false, confused, jumping to conclusions, baseless (or making baseless accusations), spiteful, malicious, mean-spirited, or (if you think someone else is influencing them) being duped.
In a communication to a court officer, you do NOT want to appear angry or spiteful, even if you are. This is why lawyer talk sounds so slippery and hollow. It still applies, though, and if the court officer has any say in the matter, they will judge the mean-spirited person more harshly.
If you have access to any kind of legal counsel, I'd definitely run it past them first. If you work in an office, there is frequently someone around who has a law degree and may find it gratifying that you asked for help (or not, depending on the person). A lot of people are members of some organization or other that they may not even realize provides some kind of legal service. Or just get an attorney, at which point THEY should be drafting any letters. This is an expensive option, however, but cheaper than insult, injury, and dishonor (in my opinion).
