In Justified, the season 2 finale, I read that Raylan has betrayed Art's trust. How did he do that?

The only thing I can think of that you might be talking about was an issue with money that was in the evidence locker. Winona (Raylan's Ex-Wife) took money in the locker and told Raylan about it. Raylan was able to get the money back into the locker but not before Art and the FBI ran it through a database that told them one of the $100 bills they found should have been in the locker the whole time. Art caught them as they were putting the money back (he didn't see them with his own two eyes but he felt something was up). Seeing it in the database tied it all together for him and he realized Raylan was a part of it, therefore betraying his trust. Sorry if this was confusing. Reading over it myself, I'm a little confused but it's the only way I know how to describe it.