I’ll be ignoring the legal aspects of your question because they are off topic here and would depend on where you live and a lot of other details.
But for the parenting aspect:
I myself and probably most of us here have been in situations where our children blew a tantrum and we thought by ourselves “if some stranger saw/heard that, they would call the authorities”. Well, in your case they did. And they came, checked on you and found everything was fine.
And that’s ok: the police did not come to your house to frame you, it’s their job to assess the situation. And I’m sure that the officers were also relieved that it was a false alarm.
As for the neighbor: You might be angry at her, but please put yourself in her shoes for a moment. We have a child that is clearly in distress, evidenced by the frequent crying and wailing. She could have reached out to you to get to know you and thereby gain insight on your situation, but not everyone has the courage (or simply the time) to do so. And I would also think twice before meddling with what could be a violent situation. But she did act. We cannot say what her motives were, but for the sake of exercise let’s assume good intentions. If you are so inclined, you could even reach out to her and thank her, explain your situation and hopefully prevent a future call to the cops. (And yes, that’s you taking the high road big time.)
The statistics are clear: Children subjected to domestic violence is still a reality even in modern societies, the number of unreported cases is high and the effects of abuse experienced as a child can and likely will influence adults’ lives. Perhaps this can help you see your neighbor’s actions in a more benevolent light. She might have been prompted to action by news reports on abuse (like some who sees crime around every corner because it was on TV yesterday), she might be the meddling type who has the police on speed dial, but she was willing to do something. Children die because adults look away.
There is one involved party we haven’t talked about yet: Your child. Did she notice what happened? I sense a great teachable moment here. “Crying wolf” can have serious side effects. Yes, if you are three years old and tired, you can’t control all tantrums. But I think it’s a good age to at least start reflecting on your own behavior - and it fits with starting school (?) where learning to restrict at least some of her impulses is part of the daily exercise. Don’t scare her (“If you don’t stop, the police will take you away!”), but if you can have fewer tantrums, not only your neighbor will be calmer, you as parents and family will benefit as well. You might want to look into the situation at school as well, perhaps find ways to make the transition easier for her or find other ways to alleviate the stress.