In addition to passing the annual budget and approving city ordinances, Boston’s City Council hold hearings – lots of hearings, on topics ranging from geese droppings to police body cameras to housing, inequality and education.

Under a proposal by City Councilor Michelle Wu, the body would also hold hearings on … whatever Bostonians want to talk about.

On Monday, a Council committee heard input on a bill proposed by Wu that would allow residents to directly petition the Council for a hearing on any topic that receives 500 or more signatures.

In other words residents, and not just Council members themselves, would have power to set the Council’s agenda.

Wu has said the idea is based in Massachusetts unique tradition of “free petition,” which allows ordinary citizens to sponsor state legislation.

And, she told her colleagues on Monday, it would be a gesture of openness and transparency of local government in a time of political cynicism.

“I think the biggest problem that our country is struggling with now is lack of trust, and lack of communication and partnership between residents, government and other institutions,” Wu said.

“This would be the direct way to make sure that we are hearing about everything that matters to people.”

The idea is not without precedent. About a dozen municipalities around Massachusetts have similar measures and, Wu said, have had largely positive experiences.

But Boston is not, as several members pointed out, most Massachusetts communities – and several Council members offered polite skepticism.

City Council President Andrea Campbell, noting the many hearings the Council has held on the issue of police body cameras alone, worried that free petition hearings could create an untenable workload for some committees.

“Frankly, it’s important to me it’s not just important that people have a petition and then a hearing – after a hearing, what are we going to do with that?”

Councilor Timothy McCarthy, of Hyde Park, was not alone in arguing that Council members already use hearings to respond to the needs of their constituents and that residents, ultimately, can speak with their votes.

“We keep saying ‘tool, tool, tool,’” McCarthy said. “A hammer’s a tool. You can use that hammer to knock in a nail, or you can use that hammer to beat someone over the head.”

“We got into this business because we enjoy engaging the community. And we all got elected because they agree that we do engage the community well enough.”