You aren't necessarily the same entity as the school. Whose tax id number was used to open the PTO's checking account? If it is the school's, or the district's, then your group is a committee of the school/district and the financial responsibilty ultimately lies with them (though ethically, it seems to be the PTO's problem, not the school's). If your PTO has its own tax id number, also called the EIN, then the school has nothing financially to do with it. Furthermore, if the PTO has its own id #, but as you said, is not incorporated, the leasing company could come to the officers personally for the money, if they really got snippy. That's why incorporation is so important, even if you don't apply for your 501c3. The next thing I'd do is go to the bank and find out what tax id number is on the account. Your school's business manager could tell you if that's the school's number, and teh IRS can tell you whose it is, also. You might even be able to look it up on their website,
www.irs.gov.
Hopefully the leasing company will accept a payment plan that works for your group. Some money is better than no money to them.
All that aside, this is a very good lesson for all of us. Our bylaws are silent on the issue of contracts/signing. We need to take a look at a policy.
Good luck.