Among other things, you really need to know:
- What is the goal of your group?
- Will your group be independent of the school or more of a specialized committee under it's umbrella?
- If you are independent, will the funds from major fundraisers belong to the PTO or will the PTO be more the volunteer organizers and the funds deposited with the school?
With a private school, the PTO often acts more like a committee and may do fundraising for items outside the role of the "typical" public school PTO. (My friend's group raised money for tuition scholarships, a new A/C, roof repairs, salaries as well as additional programs, supplies, field trips.)
If you are an
independent organization, you do need your own EIN and bank account. As an independent group, if you are likely to have more than $5000 coming into your accounts (from all sources), then you are expected to formalize and file for 501(c)(3) status by filing the 1023 application form. With less annual gross receipts, you can operate less formally and still be considered tax-exempt by the IRS, assuming you are following all their rules.
If you are an extension of the school, then you operate under their umbrella and your finances should be accounted for as one of their programs.
Here's another
discussion
that explains some of this.
Let us know more about what your organization is and we can help answer more questions.