Background check with tickets...plz read?

i'm trying to move into an apartment complex and one of the requirements is for me to have a background check done. It's only yes or no questions on whether or not i have ever been convicted of a felony, ever been arrested, or caused a disturbance and the answer will be no to all. Ok my question is i have some tickets that haven't been paid in full and i think i have warrants for them. the tickets were given to me outside city limits by the state troopers.when i go to the local PD for the BG check will i get arrested or will the secretary just bring it to my attention. I'M SAVING TO GET THEM PAID BUT I'M REALLY TRYING TO MOVE BEFORE MY baby is born. Or should i forget about moving until my tickets are paid which will take a while