Two answers to the original post.
1. Don't talk about it at the original interview unless directly asked about it. Don't you ask about either. "My cousin wanted this job but he was in jail, how would that affect his chances?"
2. When it comes time to do the personal history questionnaire, be honest, painfully honest. Have the court/arrest/jail/rehabilitation dates, case numbers, jursidictions, etc with you. They will do a real record search on you, going back forever.