This doesn't entirely make sense but my warning hackles are up. If you are going to cooperate with the authorities in this matter it would a good idea to have an attorney involved who can bring the prosecutor on board, since only the prosecutor can make binding commitments and, without such a commitment you are in danger of being double-crossed.
The only reason the police would want you to take a polygraph examination is because they suspect you of some criminal act. A polygraph is NOT admissible as evidence, and you receive no benefit from taking one; if the police think you're guilty, they will still arrest you even if you "pass".
Hire an attorney and stop talking to the police.