Jared Evans, a member of the Indianapolis City-County Council, is proud that the city is among 20 finalists for one of the most coveted prizes in the country: the planned second headquarters of Amazon.

He does, however, have one small question: What financial incentives did his city dangle in front of Amazon?

"What have I been told?" Mr. Evans said. "Absolutely nothing."

Across the country, the search for HQ2, as the project has been nicknamed, is shrouded in secrecy. Even civic leaders can't find out what sort of tax credits and other inducements have been promised to Amazon. And there is a growing legal push to find out, because taxpayers could get saddled with a huge bill and have little chance to stop it.

"The only time the public may become aware if the city has promised Amazon incentives is if we win and then we need to get those incentives passed," Mr. Evans said.

A primary reason for the information blackout is that, in many cases, the bids were handled by local private Chamber of Commerce affiliates or economic development groups that aren't required to make their negotiations public. Many of the groups are also not covered by Freedom of Information Act or state open-records requests.

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But another reason is gamesmanship. Some cities say they want their Amazon proposals to remain confidential to avoid showing their hand to rivals. And Amazon required the finalists to sign nondisclosure agreements that forbid the local groups to release proprietary information about the company.

"I don't know what we offered Amazon in terms of financial incentives, but I believe Amazon wants to see the biggest incentive package that any city will offer them," said Leslie Pool, a member of the Austin City Council. The city, also a finalist, submitted a bid put together by the Greater Austin Chamber of Commerce, which had no consultations with the City Council.

With so much secrecy — and bids like Austin's that involve unelected officials making promises — there is the risk that taxpayers and their civic leaders will be forced to accept the proposed terms or live with turning down an enormously lucrative opportunity. Amazon, which is expected to make $235 billion in revenue this year, promises to bring the winning location up to 50,000 high-paying jobs and a $5 billion investment in construction.

When the competition was announced last year, 238 places vied to be considered. In January, that list was winnowed to 20 finalists, which are now waiting to find out whether their communities will land the project. There is widespread speculation that the company could cut the field down again as soon as this month, asking for best-and-final offers. Amazon has not offered any updates, and a spokesman declined to answer questions about the process or the company's plans on the record.

The few bids that have become public are breathtaking financial packages that indicate just how much states are willing to pony up to woo Amazon. Maryland put together an $8.5 billion tax incentive and infrastructure bid, and local and state officials in New Jersey got legislative approval to offer Amazon $7 billion in tax credits and incentives to pick Newark.

But that kind of transparency is the exception.