I’m not sure where they are going by taking her statement. Yes, she falsely accused Jennifer but she had already recanted that statement which is why Jennifer was released. But, to my knowledge, lying about your baby dying is not against the law. I don’t know what she did that they needed to get a statement. Heck, threatening suicide isn’t illegal either. In some states you can be unvoluntarily "admitted" for evaluation/observation for 24 hours but not arrested.
No, I’m afraid Nicole’s only consequences now are sheer humiliation.