WASHINGTON — Law enforcement officials, members of Congress and the House committee investigating the Jan. 6 attack on the Capitol are digging deeper into the role that fake slates of electors played in efforts by former President Donald J. Trump to cling to power after he lost the 2020 election.

In recent days, the state attorneys general in Michigan and New Mexico have asked the Justice Department to investigate fake slates of electors that falsely claimed that Mr. Trump, not Joseph R. Biden Jr., had won their states. Representative Mark Pocan, Democrat of Wisconsin, wrote to Attorney General Merrick B. Garland on Friday demanding an investigation into the same issue in his state.

And this week, members of the House committee scrutinizing the Jan. 6 riot said that they, too, were examining the part that the bogus electoral slates played in Mr. Trump’s scheme to overturn the election.

“We want to look at the fraudulent activity that was contained in the preparation of these fake Electoral College certificates, and then we want to look to see to what extent this was part of a comprehensive plan to overthrow the 2020 election,” Representative Jamie Raskin, Democrat of Maryland and a member of the committee, told reporters on Capitol Hill.

The false slates, put forth in seven contested swing states, appear to have been part of a strategy by Mr. Trump’s allies to disrupt the normal workings of the Electoral College. After election officials in those states sent official lists of electors who had voted for Mr. Biden to the Electoral College, the fake slates claimed that Mr. Trump had won.

“I’ve had people in my district ask me what’s being done with these folks,” said Mr. Pocan, who forwarded the names of the 10 fake pro-Trump electors from his state to Mr. Garland in his letter demanding an investigation. “Enough people kept bringing it up. If people think they can get away with some scam, they’ll try another and another.”

Attorney General Dana Nessel of Michigan said this week that she believed there was enough evidence to charge 16 Republicans in her state for submitting false certificates claiming Mr. Trump won her state’s electoral votes in 2020. She said she had handed over to federal prosecutors the results of a yearlong investigation into Republicans who signed documents in December 2020 falsely identifying themselves as Michigan’s electors. New Mexico’s attorney general, Hector Balderas Jr., referred similar allegations to federal law enforcement. And a local prosecutor in Wisconsin also recommended that state or federal prosecutors investigate fake electors in that state.

Representative Bennie Thompson, Democrat of Mississippi and the chairman of the committee, called the fake electors a “concern.” They could also play a role as the committee considers making criminal referrals to the Justice Department.

If investigators determine that the fake slates were meant to improperly influence the election, those who created them could in theory be charged with falsifying voting documents, mail fraud or even a conspiracy to defraud the United States.

Mr. Thompson’s committee this week received more than 700 pages of documents from the Trump White House related to various attempts to challenge the election, according to a National Archives log, including a draft of an executive order calling for extreme measures.

The draft executive order, which was obtained by Politico and called for the military to seize voting machines and deploy the National Guard, was the subject of heated debate inside the White House in December, as the pro-Trump lawyer Sidney Powell and Mr. Trump’s former national security adviser Michael T. Flynn promoted wild conspiracies about voting machines. Others in the room, including the White House counsel, Pat A. Cipollone, repeatedly and aggressively pushed back on the ideas being proposed.

The flurry of interest around the actions of the fake electors comes after reports in The Washington Post, CNN and Politico revealed new details about the Trump campaign’s efforts to organize the slates. Ultimately, the efforts were rejected by Vice President Mike Pence.

Though he did not directly acknowledge the existence of alternate electors as he presided over Congress’s official count of electoral votes on Jan. 6, Mr. Pence did amended the traditional script read by a vice president during such proceedings, adding language making clear that alternate slates of electors offered up by states were not considered legitimate.

As he ticked through the states, Mr. Pence said repeatedly that the result certified by the Electoral College, “the parliamentarian has advised me, is the only certificate of vote from that state that purports to be a return from the state, and that has annexed to it a certificate from an authority of the state purporting to appoint and ascertain electors.”

It is not clear who first proposed that Republican-led state legislatures in key states that Mr. Biden won could replace the electors chosen by the voters with a different slate. But John Eastman, a lawyer who would later present Mr. Trump with an elaborate plan for overturning the election, was one of the first to bring the idea up publicly when he addressed Georgia lawmakers by video on Dec. 3, 2020, and advised them to “adopt a slate of electors yourself.”

At the time, the notion was roundly ridiculed by legal scholars who dismissed it as a futile attempt to subvert the will of the voters.

But a review of the steps taken by Mr. Trump’s allies to push the plan suggests that the effort was widespread and that it caught on among influential players, including those in conservative law and media circles and with White House aides.

At the heart of the plan was an effort to empower Mr. Trump’s allies in Congress to hand him the election. Under the Constitution, if the Electoral College deadlocks or if no candidate receives a majority of its votes, the House of Representatives decides the victor. Each state delegation casts a single vote in these so-called “contingent elections.” Under that scenario, Mr. Trump would almost certainly have won.

Central in the effort was a group called the Amistad Project, a wing of the Thomas More Society, a Chicago-based conservative legal organization. In the wake of the election, the Amistad Project worked closely with Rudolph W. Giuliani and other members of Mr. Trump’s legal team to file lawsuits challenging the vote results in key swing states.

“We are excited to have the Amistad Project as a partner in the fight to ensure the integrity of our elections,” Mr. Giuliani told a Wisconsin political website at the time.

On Dec. 14, as the members of the Electoral College were set to meet and certify electors in all 50 states, Ian Northon, a lawyer for Amistad Project, tried to deliver a false slate of pro-Trump electors to the Michigan Legislature in Lansing, but was turned away by state troopers. That same day, the Amistad Project’s director, Phill Kline, fanned across right-wing media outlets promoting the fake elector plan.

On a podcast run by Stephen K. Bannon, a former adviser to Mr. Trump, Mr. Kline declared that only state lawmakers had the power to decide who should be electors, “not governors or local election officials or even the Congress of the United States.”

Mr. Kline also appeared on One America News, the conservative television network, saying that if dueling slates of electors cast doubt on the results of the election, then the House of Representatives would get to decide who won — and that would lead to a victory for Mr. Trump.

Some of Mr. Trump’s own aides were pushing this same gambit. As the Electoral College gathered to vote, Stephen Miller, a top adviser to Mr. Trump at the time, announced on Fox News that state lawmakers in several “contested states” were sending “an alternate slate of electors” to Congress.

“This will ensure that all of our legal remedies will remain open,” Mr. Miller said.

Even after the Electoral College certified Mr. Biden’s victory, ignoring the fake slates, Mr. Kline and other allies of Mr. Trump did not give up the fight.

On Dec. 22, 2020, the Amistad Project filed a federal lawsuit claiming that the state lawmakers whose alternate slates were rejected had been “prohibited from fulfilling their constitutional responsibilities.”

The lawsuit — which was ultimately dismissed — sought a judicial order that would have essentially forced Mr. Pence to acknowledge the fake electors on Jan. 6, 2021, when Congress met to issue the final count of the Electoral College results.

Mr. Kline could not be reached for comment, but he posted a message on Twitter on Tuesday condemning Ms. Nessel for what he called “trumped-up charges of ‘forgery’” with respect to the fake electors in Michigan.

“The timing of this attack — more than a year after the fact— shows that it’s purely political,” he wrote.