Candy, the police may have certain protocols but are not neccessarily trained too well in other ways and they have a narrow view in legal terms. If you called a child and family service agency or a crisis hotline, they could direct you toward a qualified specialist who is better trained and hopefully far more competant. You are correct to follow with caution but you are doing the right thing to make inquiries. I hope this helps and there are local services where you live. One last thing, a 3 year old has no knowledge or experience to fabricate such tales and that sure seems like enough to warrant further investigation at any cost.
When you stumble, make it part of the dance.