There's quite a bit of content in your question. I'll break it down.
First of all, the tax exempt number you have probably is a "tax identification number" (a.k.a. TIN) issued by the Internal Revenue Service. It's like a social security number for a person. Any business can get one, for free, and it's just an identification number. It doesn't imply any sort of tax exemption. Tax exemption is a separate process.
You mention that you are a public school. Yes, a public school is automatically exempt from federal income tax ("tax exempt"), but a PTO that operates independently from the school is not. However, if your PTO is banking under the school's tax id number, which is quite possible though not always advisable, then your PTO is just a subset of a tax exempt organization (the school). Some PTO's do that consciously because they and the school have deteremined that's the best way for the two entities to coexist. Other PTO's use the school's tax id number innocently thinking it can apply to the PTO too. In either case, if the PTO's money is held in a bank account opened using the school's TIN, the money technically belongs to the school, not the PTO. Still other PTO's get their own tax id number from the IRS and keep their money independent of the school.
The letter that your donors is asking to see is the "determination letter" issued to a federally-registered 501c3 charity. The IRS sends one out when they approve your Form 1023, the application for 501c3 status. There is no fancy "tax exempt certificate" nor new number issued by the IRS when you get 501c3, just a dull multi-page letter explaining the rules. However, this letter (and sometimes just the cover page is all that's needed) assures a donor that you are a federally-recognized charity.
I know our PTO has a determination letter because we filed for our own 501c3 status. I'm not sure where I'd look for a copy of the school's determination letter (if our POT was a substet of the school) - maybe the school district business office.
Now.....if your PTO is really operating as an independent organization (that is: managing its own money, own bylaws, own officers, sets own budget) and if you already have your OWN tax id number, then you need to file FORM 1023 to complete the process to become a federally-recognized 501c3 charity. It's a complicate form, and the one-time filing fee is $750, but that makes your PTO a real tax-exempt charity. (Caution: there are rules you must follow when you're a 501c3 like filing the annual IRS form, so it's not a step to be taken lightly). Once you get 501c3 status, donors can donate to you like they do any charity.
On the other hand....if your PTO is operating under the shcool's tax id number, then everything you do runs thru the school and donors are donating to the school, not your PTO. You would want to emphasize that when seeking donations (you might even want to have your principal sign the donation request letter so the prospective donor feels assured s/he is donating to a public school).
And finally....if your PTO is using hte shcool's tax id number, but is trying to operate independently from the school (ex: you have your own bank account), then it's time for your PTO to seriously consider getting your own tax id number from the IRS (free, fill out Form SS-4), and then filing for your own 501c3 status.
There's lots of past discussion about 501c3 on this message board. You could also order the PTO Today start up guide which explains the 501c3 stuff in detail.
