Yes. If you are convicted at a General or Special court-martial, the conviction will likely go on your criminal record. Depending on the type of court-martial and the exact charges, they may appear as Federal felony convictions or misdemeanors. Some military-specific crimes with no civilian equivalent may or may not appear as Federal convictions on a state arrest record. However, as a general rule, assume that all General and Special court-martial convictions will appear on a criminal background check.