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I know you have addressed background checks before. Specifically, if, on the application, it asks about felonies or misdemeanors involving instances not related to a DWI:
-Should I bring this up on my own?
-Should I wait for them to bring it up since they are running a background check?
You're right, we have done this before (go read the comments on that post for more insight). Given that, I really wish you could have told me a little more about what exactly you were convicted of just for my own purposes (I'm curious). Not all charges are created equal, as I'm sure you know. If you violently stabbed a classmate with safety scissors at 12, perhaps that should be disclosed. If you got busted with an open can of paper-bagged PBR in the park at 20, that's something entirely different. Your chosen alias tells me your convictions probably have something to do with weed, alcohol or other bro games, in which case you'll probably be fine since it is a known fact that public accounting consists of approximately 65% bros, either current or reformed.
From the perspective of the firm, is your checkered past something that directly impacts the job they'd hire you to do? Anything financial, unethical or exceptionally terrible should probably be disclosed before they have a chance to uncover it. Does that mean you should blurt it out during the first interview? I'd say no, I had a candidate do that to me once and must admit it came off as awkward and slightly inappropriate. Safe to say he did not get the job and his petty little weed problem had nothing to do with it. So it's all about revealing it at the right time and to the right people.
Chances are they are not going to run the background check right away. By disclosing it up front, you save yourself a really awkward conversation months down the road when they call you in to discuss the interesting results.
I think the bigger issue is going to be honesty, not the charges themselves, assuming you didn't do anything really awful like intentionally run over a family of four or burn down a school or anything like that. Since the application asks for it, you should probably provide it but take advantage of the space they give you to explain the situation. Once you've done that, you're clear, there's no need to go out of your way to explain your story to every person at the firm you come in contact with.
I'd also suggest you avoid dismissing or minimizing your past in your explanation. Be honest (not TOO honest, keep it short and simple) but show a little responsibility for your own life in the process. Blaming others (e.g. The Fuzz) won't earn you any points and you're already working against yourself to stand out as exceptional despite your sketchy past. Hopefully this was a few years ago and you can share how you used it as an opportunity for personal growth. You know, learned your lesson and all that.