Depends on the police department.  Most PD's don't require that you tell them up front of a failed poly.  But almost every single polygraph examiner will start by asking you "Have you ever taken a polygraph examination before and what were the results?"  They do this so that they can use this information as a tool to produce an accurate result.  Normally if you have already failed a polygraph exam then if the examiner knows this he will fail you again to produce the fact that the polygraph is "accurate".  If you failed on polygraph and pass another then you just proved to the world the thing is a joke and they don't want that to happen.  Your problem is if you lie and through the background check they find out that you did take one.....guess what happens next?  Sorry if this scares you but this is reality.  This is the reason why this web site exists.