No, the state PTA can't access your funds. They might ask for them, but they can't take them from your account. How easy this process goes seems to depend on the particular state PTA. One way a lot of groups handle it is to start the PTO while the PTA is still running. You'll need an EIN and a separate bank account for the PTO.
The PTA continues to operate, with the money being spent as needed -- quickly or over time, depending on how much money is involved. Meanwhile, any fundraising is conducted by the new PTO and money raised goes into the PTO account.
- Craig
Links in this post: