Hire an experienced criminal defense attorney ASAP. You have no obligation to make any statements whatsoever. "Lie detectors" are notoriously inaccurate and inadmissible in many states. Do not speak to anyone about this other than a defense attorney.
This answer is offered for informational purposes only. It is not offered as, and does not constitute, legal advice. Laws vary widely from state to state. You should rely only on the advice given to you during a personal consultation by a local attorney who is thoroughly familiar with state laws and the area of practice in which your concern lies.
CPS investigations are different from any other, and CPS investigators neither use the same rules of evidence or the way they handle their cases as police officers. You should immediately contact a family lawyer in your area to represent you in further dealings with CPS.