Bills designed to protect public schools from liability so they will be more willing to share fields and gyms for kids’ sports leagues have run into surprising opposition: lawyers for the schools.

At issue in the General Assembly is an idea pushed by the American Heart Association to open up more recreational facilities as a way to fight childhood obesity. The identical measures, Senate Bill 12 and House Bill 382, require outside groups using school facilities to obtain at least $1 million in liability insurance coverage and agree to hold harmless the school’s governing authority.