Portuguese immigration officials, just like their other European counterparts, require an official proof of absence of criminal record from you. It's obtained from the countrye, where you spend the last 1+ year. Usually, it's requested from the federal government and needs to be apostilled and translated into English or Portuguese.
If you're applying from the US, we can help you obtain your criminal record quickly and apostille it.
BTW, Portuguese authorities should not count minor offenses in your record against you if similar offenses are not punishable in Portugal by incarceration for over 1 year.