Credit Check -- Background

[treetop]

I recently received a background packet to fill out with a local LE agency.  In it, it asks for me to list all accounts that have ever been turned over to collections.  I have had several accounts turned over to collections, however, I recently received my credit report from Transunion, Experian and Equifax and there is no record or mention of these accounts.  If I mention that I had several accounts turned over to collections and only recently paid them all off, will that hurt my chances of being hired?  Secondly, if I do not mention that any of these accounts went to collections, will they find out that they did even if it is not on the three credit reports I received?   Any thoughts?  Also, does TRW, the old credit reporting agency still exist or are the three credit reporting agencies I mentioned above the only ones the investigator will look at?