By Rolfe Winkler

May 24, 2016 5:30 a.m. ET

For more than a year, Jay Biederman has pestered Domo Inc. for its financial statements. The former executive wants to estimate how much his tens of thousands of shares in the tech startup are worth.

Domo, whose software analyzes corporate data, has rejected those requests, he said, keeping its financial records under wraps like most privately held startups.

But the law may be on Mr. Biederman’s side.

He recently discovered section 220 of Delaware’s corporate law, which can compel locally incorporated companies such as Domo to open up their books to shareholders. The law, little known in Silicon Valley, is a potentially valuable tool for thousands of tech workers who received stock awards to join fast-growing startups, as well as other small investors, who now question their shares’ worth.

To take advantage of the law, stockholders must simply prove they own at least one share and send the company an affidavit that states which documents they want and why. The magic words for unlocking financial information? “ ‘For the purpose of valuing my shares,’ ” says Michael Halloran, a securities lawyer with Pillsbury Winthrop Shaw Pittman LLP.

Companies must then comply or face the possibility of legal action. Shareholders are backed by strong case law, say lawyers. To keep their financial data private, companies often ask the shareholder to sign a nondisclosure agreement.

Valuations of private tech companies are in doubt after years of hype and seemingly endless cash from venture investors lifted values to new heights. Many of those investors are now stepping back, pushing startups to deliver profit over growth. Mutual-fund firms are marking down their stakes in some startups, adding to the confusion. And the market for tech initial public offerings is all but shut, another sign startups are overvalued.

As companies stay private, their financials remain concealed. Only top investors typically receive periodic updates on revenue, profits and financial projections.

Some highly valued companies, such as software firm Palantir Technologies Inc. and ride-hailing company Uber Technologies Inc., share little if any information with smaller shareholders, say people familiar with the matter. Spokeswomen for the two companies declined to comment.

Companies say keeping their financial information private, even from some stockholders, prevents it from falling into rival hands. The lack of public scrutiny also gives them freedom to invest for the long term.

With at least 145 private companies including Domo now valued at $1 billion or more, the financial secrecy has caught the attention of the Securities and Exchange Commission’s chairman, Mary Jo White.

“Our collective challenge is to look past the eye-popping valuations and carefully examine the implications of this trend for investors, including employees of these companies,” Ms. White said in a March 31 speech, while also raising concerns about the accuracy and availability of financial information.

There have been hundreds of Delaware lawsuits to inspect company books says Ted Kittila, an attorney with Greenhill Law Group. Most requests are settled before a suit is filed, he says.

Some companies are now pushing employees to waive their right to inspect the books as a condition for receiving stock awards, says Richard Grimm, an executive compensation attorney. Fitness tracking company Fitbit Inc. and online dating site Zoosk Inc. both did so as private companies, according to their IPO filings. Fitbit declined to comment. Zoosk didn’t respond to questions.

“It’s unclear whether this kind of waiver would be supported” in court, Mr. Grimm says.

Option holders at some larger private companies are supposed to receive financial information upon request, according to an SEC rule. It is unclear whether all private tech companies covered under the rule are complying, lawyers say.

Chris Biow, a former executive and shareholder at MarkLogic Inc. and MongoDB Inc.—two software startups valued at over $1 billion—says he regularly discusses Delaware inspection rights with groups of employees for each company.

“We have all these ‘unicorns,’ where it’s not clear what year or decade they may go public,” said Mr. Biow, now a senior vice president at Basis Technology Corp., using a tech industry term for private companies valued over $1 billion.

Mr. Biow said he wants to know the revenue and profits as well as the list of stockholders, which may be the only possible buyers of his shares as private companies often restrict sales to new investors.

San Carlos, Calif.-based MarkLogic, valued at $1 billion by investors a year ago, eventually agreed to let Mr. Biow view its financial results in its office in 2014, though it has refused to share a full stockholder list, he said.

A MarkLogic spokesman said the company’s practice “is to be forthcoming with our financial information for any shareholder that makes a proper request to the company.”

Mr. Biow only recently exercised his MongoDB stock options so he hasn’t yet asked the New York company for information.

Meanwhile, Mr. Biederman, who left Utah-based Domo in February 2015 after four years, says he is still trying to get information from the company. This January, Domo’s treasurer denied access, saying it wasn’t sharing financial data with stockholders, Mr. Biederman said. A month later he submitted an affidavit citing his rights under Delaware law.

Since he filed the affidavit, two divergent signals have exposed the difficulty in valuing his shares. In February, Fidelity Investments marked down its Domo shares to $5.03 a share, 40% below where the company previously sold shares that equated to a $2 billion valuation. A few weeks later, in March, Domo said it raised more capital at the same $2 billion valuation, and Fidelity subsequently marked its shares back up to $8.43 a share.

Then last week, trading firm EquityZen Inc. sponsored an offering to buy shares from employees at $6.36, according to a presentation reviewed by the Journal. An EquityZen spokesman declined to comment.

Mr. Biederman, who last year exercised his options at 32 cents a share, said the company has asked him to sign a nondisclosure agreement before sharing financial information. He says Domo has yet to send it to him.

A Domo spokeswoman declined to comment.

Write to Rolfe Winkler at rolfe.winkler@wsj.com