My question involves a background check in the State of: New Jersey

I am applying for a position that requires a background check. I stated on the application that I was still currently employed because I was too embarressed to say I was let go 3 weeks ago. And although I checked the box that says that they can't contact my current employer...I'm concerned that they will somehow find out that I'm no longer employed. Is there anyway that they can discover my dates of employment at that company...if they don't contact them?
Any help would be greatly appreciated.