Employment Verification and Background Checks

[Traveltime]

I am applying for a police dept. in PA that will be doing an employment verification check. I worked for another dept. last year for a month and things didn't work out there. That dept. never completed my certification process so it dosen't show in the state system MPOETC that I was there. If I don't put that on my application or tell them about it, can they find out about it by the verification or the background check? Thanks!