Paying for something does not, by itself, make someone liable: for example, if I, as a parent, give my over-18-year-old daughter money to buy a car, but I am not on the car's title, do not insure it under my name, and am not an owner, I am not liable if she gets into an accident while driving it. Liability is generally based on fault, which generally goes to the party which had control but was negligent or careless in some way. Unless the PTA actually controls the buses (e.g. hires the buses and therefore exercises supervisory authority over the buses and drivers), they would not be liable. That is the general rule. It is possible for liability to be set or apportioned by contract, so if the PTA signs an agreement agreeing to "indemnify" the district for any costs or liability, by doing so, they would make themselves liable.