I know it's tempting to want to leave it off, however don't do it!
Dh has a criminal record from 23 years ago, when he was a minor. We disclosed to our agency who decided to leave it off the homestudy. When the agency pulled a background check, it didn't show up. She was under the impression that it would be better to not open the can of worms in relation to the country we were adopting from.
Long story short -
INS pulled a criminal background check & it appeared. Since we didn't list it on the homestudy, they stated they had serious doubts of our ability to parent. This resulted in them denying our I-600a.
The agency appealed, stating we did disclose to them. However, there are very specific steps the agency needed to take for the appeal (which they didn't do), and as a result, our appeal has been dismissed. The agency is trying to appeal the appeal, however, I've been told we have to wait a year to reapply. Even if we do reapply (& this time adjust the homestudy to reflect the prior arrest), there's a strong chance that since we were denied before, they'll still deny it.
Unless the "trouble" your dh was convicted of was child abuse, child molestation, or extreme violence, strong chance it won't hurt you guys.
Check out this link:
http://www.access.gpo.gov/nara/cfr/w...cfr204_04.html
click on the 204.3 "Orphans" link - this will go into depth on what exactly needs to be in the homestudy.