Last week, the Las Vegas City Council ended a weeks-long stalemate by awarding a construction contract for its proposed mob museum to APCO Construction. APCO was supposed to earn the job last month, but rival bidder Flagship Construction filed a protest with the city that delayed the decision until July 1 but didn’t, in the end, change its outcome.

Officials at Flagship mulled their options over the Fourth of July weekend before deciding, on Monday, to file suit in District Court, seeking an injunction to halt the construction contract from moving forward. Flagship VP Teresa Bolsendahl says the filing seeks to challenge a “flawed” bid process.

It’s the latest wrinkle in an increasingly complex saga behind the scenes to renovate the old post office building Downtown into a $50 million museum meant to help jump-start economic development in Downtown.

APCO, Flagship and other companies first submitted bids to the city last fall. In the first bid, Flagship was the low bidder; consequently the company still thinks it should have gotten the job. Flagship contends APCO helped sour the first bid by complaining about its competitors’ qualifications. But Randy Nickerl, APCO’s manager, says the city decided to rebid the contracts on its own, because, he says, “None of the contractors met the experience requirement for working on historical buildings.” (Including APCO.) The city, he says, threw out the bids and relaxed its qualifications.

In the second bid, earlier this summer, APCO came in at $11.5 million, around $1 million lower than its initial bid. Bolsendahl refers to the reduction as “crazy low.” She says Flagship and the other bidders all lowered their prices between 2008 and 2009, but not nearly as much as APCO.

“How do you get back 10 percent in an industry where people are making less than 1 percent?” she asks.

Nickerl says APCO’s low $11.5 million bid is legit. “It would have been nice to have an extra $900,000 on there. But we went in tight and nobody showed up. We went out there to kick butt and no one showed up. We’re okay with our number.”

It’s unclear how long it will take the court to decide on Flagship’s filing—the company doesn’t know, either, since this is the first time it’s made such a filing—but this kind of action may become more common if the economy doesn’t pick up.

“With the economy turning down, you’re going to see more and more bid protests,” says John Mowbray, an attorney representing APCO. “It’s become a very competitive market. When the town was flush with work, I don’t think you saw that many. In this day and age, if you can come up with a technical argument to knock someone out that’s lower than you, there’s an economic incentive to do everything in your power to do so.”