Well, background checks for general volunteering and an interest in PTO volunteering are separate issues. You could check with the district about contacting the "checked" volunteers to see if they're interested in the PTO, or if in the future the background check form could include something like "are you also interested in PTO volunteering?"
Our school district mandates that volunteers require a background check. Our school pays for the background check. The school has a list of 95 pre-background checked volunteers but I am unsure if the PTO is allowed to use this list of volunteers? On the volunteer interest form the school sends out there is not an option for a PTO area of interest, but if the background check is already on file why do it again?