PORTLAND — A four-story structure that has been the topic of intense speculation in Connecticut arrived in Portland by barge shortly after 7 p.m. Thursday.

People in Maine remain as confounded as their Connecticut counterparts about what it is, who it’s for and where its final destination will be.

The head of the firm due to receive the building in Maine was just as cryptic about the project as his predecessors in the Nutmeg State, saying only that it’s “very important.”

The mysterious box-like structure was built by Turner Construction at the Adm. Harold E. Shear State Pier in New London, Conn., and was shipped out from that location on a barge bound for Maine’s largest city around midday Wednesday, The Day newspaper of New London reported.

The Day reported that the barge was accompanied by a Portland Tugboat LLC tug on its voyage, and that around Connecticut waterfront circles, the building was rumored to be anything from a movie set to a floating prison to a top secret Defense Department project.

Whoever is commissioning the project is insistent on keeping details shrouded in secrecy. A spokesperson for the pier terminal told the Connecticut newspaper that Turner Construction has been “very adamant” about “keeping it under wraps.”

Nicole Clegg, spokeswoman for the city of Portland, said the city won’t be involved with the project.

The barge carried the structure along the waterfront to Rickers Wharf Marine Facility in Portland, which is operated by Cianbro, a Pittsfield-based contractor.

Cianbro CEO Peter Vigue told the Bangor Daily News the project is “very important,” and acknowledged that Rickers Wharf was the destination of its voyage from Connecticut. But Vigue said he couldn’t confirm what kind of work his company is doing on the building.

“The facts are that I’m not at liberty to discuss the project in any detail,” Vigue said. “That comes at the request of our client, who has not and will not be identified at this time.”

The Cianbro executive suggested that the mysterious project could lead to more work for the Maine company if successful.

“We can’t jeopardize the client’s current position on this project or our potential opportunities as well,” he said.

John Henshaw, executive director of the Maine Port Authority, said that although he doesn’t know what this specific project is, it doesn’t appear completely alien to him.

“It looks similar, at least from the picture I saw in the paper, to other modularly constructed buildings that Cianbro has worked on in the past,” Henshaw said, referring to a 2009 modular refinery project in Texas and a more recent Newfoundland nickel mining project build.

The last of the 22 modules in the Newfoundland project were shipped out from Brewer last year. That project employed more than 100 workers, Vigue told the Bangor Daily News at the time.

Modular structures — whether homes or more industrial buildings — are generally constructed using large, plumbed and wired puzzle pieces of sorts that were assembled off-site and then fitted together to make a single building at a desired location.