Tax Exempt Rentals

The library is chartered as a school district public library and thus exempt from NYS sales tax. Due to a mold issue we ended up having our HVAC contractor rent two humidifiers for us, the contractor made the arrangements and we paid for the rental via the contractor. The contractor told the renting business that we were tax exempt. The renting business refuses to remove the sales tax. They claim that the sales tax exemption only applies to purchases and not rentals. I have not been able to find anything that verifies the claim of the renting agency.