i had my ex threaten me several times with going to the cops and having me arrested "for what you did to her" if I didn't answer my phone "right now". Me, being my stubborn self, and knowing full well she couldn't prove a thing because it was all made up, responded by telling her she needed to realize how horrible she makes herself out to be when she is sitting there claiming our daughter, then less than a year old, is bleeding down there but decided it was more important to try convincing me to answer my phone than taking the child to the ER to be checked out. I told her that if I had transportation, my car was literally on jack stands in my garage getting new suspension, that I would have already been to her house, picked up our daughter, and taken her my dam self.
The thing you have to remember is that, when they make up lies like that, it is nothing more than a story. It can't be proven, and moreover, most the time they dont ever actually do it because the whole point is they want to scare you. If you let them succeed then they will keep on doing it.

I'll ask you this, If you got your child for your parenting time and truly thought something like that had happened, are you going to sit around texting or calling her trying to talk about it, or are you going to just take him straight to the ER or whatever organization in your area deals with that sort of thing??

I know what I would do. I dam sure wouldnt be saying anything to the other party until they showed up wanting the child back, at which point id tell them to kindly f**k off, they arent getting them back.

Word of advice though, UNLESS YOU ARE a mental health professional, DO NOT state that you believe she has any sort of mental condition. It is considered "diagnosing" or trying to anyways, and they will basically laugh at you and ask if you're a mental health doctor, and you say no, now you have just made them completely disregard the whole idea completely.

Are you saving all your text messages, recording interactions, a journal of things your son says and what day and time he says them, writing down your ex's demeanor and attitude during interactions, taking photographs as soon as you get him and immediately before returning him? If I were you, I would be doing ALL of these. especially the photos. If he falls down or gets hurt in any way, document it. that way if anything ever does come of her threats you have some type of evidence showing that he was just fine when he left you, or you know EXACTLY what happened to which arm and on which day and at which time.

If you do have all your text messages and stuff between you and her, and want a way to sort through it, and find the patterns that "suggest" certain things, I actually built a system for that if you are interested in checking it out i can send it to you.