I must confess I don't understand the polygraph requirement either. The best estimates that I have read are that they are only 90% accurate at the most. There are an estimated 4 million tests given every year in the U.S. That means that every year 400,000 people are either lying and getting away with it, OR are unjustly being accused of lying. There is a reason it's not admissable in a court of law.
I took one years ago for a correctional officer position. The admin there told me that when I was asked if I had ever committed theft, to answer "yes." I said, but I really never HAVE stolen anything, and she asked if I had ever taken a pen or pencil home with me in my pocket from work. I said "sure", and she said, "well then, you're a thief!" !!
I couldn't believe it. When the question came, I said "NO!" anyway, and the operator looked at me a bit strangely, but my response "did not indicate untruthfulness", so they had to eat it.
I ended up not getting the position anyway (in retrospect, Thank God!), but it was an interesting experience. I hope it works out well for you Gin. You would be a real asset to the Department, and who knows what your volunteer work would lead to down the road!
Good luck,
Norm