New York Gov. Andrew Cuomo called on two state agencies Wednesday to investigate Intuit, H&R Block and other companies that prepare tax returns, citing recent media reports that the companies allegedly hid their free tax filing options from Google searches.

"The allegations against these major tax return preparers are disturbing, and New York will not stand idle as the public's interest is undermined in order to pad the profits of wealthy corporations," Cuomo said. "I am calling on the Department of Financial Services and the Department of Taxation and Finance to investigate these claims to help ensure New Yorkers are protected."

Americans who make an adjusted gross income of $66,000 a year or less are eligible to file their tax returns for free under the Free File Alliance — an agreement between the IRS, major tax preparation companies and states, including New York. The partnership was an exchange for the IRS promising not to create its own free, online service.

But Intuit, the maker of TurboTax, and H&R Block are actively steering taxpayers away from their free versions — TurboTax Free File and H&R Block Free File — according to a report Sunday by ProPublica. In order to do so, the companies are allegedly adding code to tell Google and other search engines not to list the free versions of their online tax filing tools.

Intuit disputed the report's findings.

"Our search and marketing practices around the IRS Free File program have been called into question. These characterizations are untrue and we look forward to sharing the facts with New York regulators," an Intuit spokesman said in an emailed statement to CNBC.

H&R Block defended its role in the Free File Alliance.

"H&R Block's Free File program grew 8.3 percent this tax season, exceeding the Free File program growth of 6.8 percent, and we believe H&R Block is in full compliance with the Free File agreement," Susan Waldron, a spokesperson for the company, told CNBC.

Shares of H&R Block were down 2.6% to $26.50 on the news. Intuit's stock also fell, dropping 2% to $245.97.