A visitor discovered the marijuana plants growing in the flowerbeds nearby the offices of politicians, according to reports.
Above video: The medical cannabis debate in Australia
Almost three dozen cannabis plants have been found growing in the garden of a state parliament house in the US.
Police were tipped off by a visitor to the Vermont Statehouse. Police then discovered 34 plants thriving in the flowerbeds that line the footpaths near the building.
In Vermont, possession of small amounts of marijuana for recreational use is legal, but it remains illegal to grow it in public.
It was the first state to legalize recreational marijuana through legislature as opposed to by ballot in 2018 and legalized medicinal marijuana in 2004.
Vermont Capitol Police Chief Matthew Romei told CNN he does not anticipate a criminal case without anyone claiming responsibility for the plants.
"We also have no thoughts on why someone would plant it," he said.
"But if anyone wants to claim it and let us know why they planted it, we are happy to listen."
Chief Romei said he knew the story "had grown legs" when he began receiving messages from people around the country.
"I guess this is probably my first time making CNN," he said on this Facebook page.
"That said, the offer stands, if anyone wants to claim it, we are happy to make an appointment for you to come by."