Your new PTO is going to need its own set of bylaws. Usually, some kind of organizing committee would propose bylaws. That same committee would call a first meeting (of the new organization) and present the bylaws for approval.
Those new bylaws should contain some provision for first officers ("they shall be mary, sue and bill" or "nominations should be taken from floor at first meeting and election will be held that night") as well as provisions for long-term election policies that are more general than the first set ("elections will be held at the April general meeting, yadda").
Provided everyone is in agreement, it's not uncommon for a group going from PTA to pTA to use the existing PTA board as the first board for the PTO to serve until the first regularly scheduled election. Just put it in your bylaws somehow.
Several years ago we switched from a PTA to a PTO. We asked if anyone wanted to run and as usual no one came forward. So we just announced the officers of the new PTO.
Cyndy
The PTO and the PTA are two separate legal entities. You need to have new elections, although the same people can be the PTO's officers as are the PTA's officers. I think, but am not sure, that if the officers run unopposed, you can end up just appointing them instead of going through an actual election, but that's a Robert's Rules of Order question. Someone else here may know the answer to that off the top of their head, but I don't for sure.