Can my former employer go into detail with the unemployment office over why I was fired?

I'm just asking cuz I was fired from my job of two years on Thursday and I'm applying for unemployment. The reason they fired me was because of an "integrity issue", and I was fired for something that was really petty, and I was basically accused of doing something I didn't even know was wrong in the first place. What I want to know is when the unemployment office gets a hold of my employer, can my employer legally tell them what I was fired for and give them all the details of it? I'm asking because I know I'm probably really going to have to fight to get my unemployment and they'll probably deny me. And I'm worried that this is going to go on my record and really hurt my chances of being able to get another job. Wouldn't it be illegal for them to get into all the heavy details of what happened, cuz if they did couldn't I turn around and sue my former employer for slander or defamation of character?