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I am sorry to hear about this situation, Katie.
CPS does not have any specific powers itself. All CPS has is a mandate from the state to act on behalf of the child in a Court of law, i.e. as an interested party. So they can file to take custody of the child, but of course, only if there is a good-enough reason.
Normally, CPS has the Court's ear, but not always. It is not uncommon for the Court to deny CPS.
CPS also works very questionably. It is not unusual for them to use scare tactics, questionable diplomacy, and even outright lying in some cases to get what they want. They will even ask you to sign something that you may not fully understand, only for that to turn out to be a document releasing custody (that they then file with the court). So they can be ruthless.
But again, all they are - are a party before the Court with an interest in the child. Just like you.
What CPS normally does is get you to agree to a parenting plan. If you fulfill it, they leave you alone. If you do not, then CPS may file in court to ask the Judge to force you to fulfill it, or in cases of serious neglect/abuse, to try to take custody of the child.
Even if one signed that parenting plan, one may break this informal agreement at any time. But of course if one does, then CPS may try to go back to court and state "see, she is endangering the child..."
At this time, if CPS is asking too much or is exaggerating the issue, you may wish to send a certified letter stating that the matter is over and that you are not endangering or abusing the child and that CPS has has enough proof of this. And that, one will cease cooperation. CPS may go to court (there is a risk), or they may simply close the file.
It is best to use an attorney to send such a letter.
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