I got arrested for dui still pending in court. I started a job and I have to get a criminal background check for my job will this show up? This is my first time arrested. I live in Ohio

It won't show up until you have been convicted.

Not sure about OH but in NY a pending arrest will show up on a background check

There are many levels of a background check and who is the background check being done though,

Will it be done though the police department or will it be though a private research background firm ?

And who are you going to work for, some positions, such as those requiring national security backgrounds, police, some other law enforcement positions, will have a background that shows even things arrested for but that you were found not guilty or charges dropped.

Also did you apply after of before the DUI arrest.
Does you new job rely on your drivers license, such as a driver, so if your license is suspended for a month will it effect your job ?

But in general, the police background to general public only shows convictions not arrests.