4/10: This post has been updated with response from Whitehouse’s office.

A Democratic senator is pushing for an investigation of nonprofit groups that told the Internal Revenue Service they would not engage in political activity — and then spent millions attacking or praising candidates in 2012 elections.

Sen. Sheldon Whitehouse, D-Rhode Island, said at a campaign finance hearing yesterday that there were “numerous instances” in which nonprofit groups may have made false statements to the IRS about whether they planned to be involved in federal or local elections.

Applications for tax-exempt status are submitted to the IRS under penalty of perjury. If the IRS is not well-suited to investigate these “plain vanilla criminal cases,” the U.S. Department of Justice should, Whitehouse said.

ProPublica has reported extensively on the gap between what these groups told the IRS they would do in their applications for tax-exempt status and what they actually did.

Part of the benefit of being recognized by the IRS as a 501(c)(4) nonprofit is that these “social welfare” groups do not have to disclose their donors publicly. But in order to quality as a 501(c)(4), groups cannot make influencing elections their primary activity.

In 2008, Western Tradition Partnership, now known as American Tradition Partnership, told the IRS that it would not attempt to sway elections. Shortly before submitting this application, it had blitzed Montana voters with fliers weighing in on candidates in the state’s Republican primary. After the IRS approved the group’s tax-exempt status, it continued to send out fliers supporting or opposing candidates in both Montana and Colorado.

Similarly, the Government Integrity Fund told the IRS in 2011 that it did not plan to spend any money influencing elections. Then, in 2012, the group spent more than $1 million on ads attacking Ohio Democratic Sen. Sherrod Brown and praising his Republican opponent, Josh Mandel.

When Arizona-based Americans for Responsible Leadership applied for tax-exempt status in 2012, the group had already spent $5,300 on get-out-the-vote efforts for Sen. Orrin Hatch, R-Utah, and given $57,500 to two Republican political committees in Arizona.

But it told the IRS in a confidential filing that it had not spent any money, and did not plan to spend any money, influencing state, local, or federal elections. The group would go on to spend $5.2 million on campaign activities in the fall of 2012, most of it on phone calls urging the defeat of President Barack Obama.

After ProPublica ran a story on the group, a lawyer for Americans for Responsible Leadership told the Arizona Capital Times that the group had submitted an “amended application” to the IRS that “corrected the error.”

The Government Integrity Fund told ProPublica that it worked hard to be in compliance with the law and that “Legally, the concept of ‘influencing elections’ has been narrowly defined.”

And the American Tradition Partnership’s executive director said that ATP had obeyed all applicable laws and “does not, and never will, tell voters which candidates to vote for."

At the Senate Judiciary Subcommittee hearing on campaign finance law enforcement hearing, Whitehouse did not mention any nonprofit groups by name, but he cited ProPublica's reporting on these groups at length in his introduction to the hearing, as his spokesman noted.

Whether or not the IRS or the Justice Department is already investigating any of these groups is not clear. Representatives who testified at the hearing would not comment on any ongoing investigations.

Larry Noble, the president of Americans for Campaign Reform, said at the hearing that the IRS and the Justice Department were hesitant to enforce the laws on the books because of “fear of getting involved in politics, fear of being called partisan when you’re not.”

Mythili Raman, the acting assistant attorney general for the Justice Department’s criminal division, testified that the rise of new 501(c)(4) groups active in politics increased the risk of “bad actors using the anonymity that’s given to them when they donate” to corrupt the political process.

Raman said that the department needed more transparency in order to enforce anti-corruption laws—as well as a clearer definition of “coordination.” Super PACs and 501(c)(4) “dark money” nonprofits can raise unlimited amounts of money, but they aren’t allowed to “coordinate” their advertising spending or other political activities with candidates’ campaign. Proving coordination, though, isn’t easy.

“We simply don’t have the tools to tell if super PACs are illegally coordinating with campaigns,” Raman testified.

Part of the issue, she said in her prepared testimony, was that the Federal Elections Committee has failed to define whether certain activities— like a candidate’s mother running a super PAC expressly supporting his candidacy—count as coordination.

Whitehouse also pressed for investigations of whether individuals or organizations had created “shell companies” or used 501(c)(4)’s to donate money to political action committees in order to avoid disclosure requirements. Americans for Responsible Leadership is currently under investigation in California for what a state watchdog group called “campaign money laundering.”

Sen. Ted Cruz, a Texas Republican, said at the hearing that aggressive enforcement of campaign finance laws might restrict free speech. He cautioned against any “prior restraint, or punishment after the fact” for citizens who choose to speak out against their elected officials.

Cruz said that Organizing for Action, a continuation of Obama’s reelection campaign that is now operating as a 501(c)(4) nonprofit, was currently running ads against him, and that his campaign for Senate had been on “the receiving end of $35 million in attack ads.”

“God bless them for speaking out and being involved in politics,” Cruz said.