WASHINGTON — President Donald Trump’s sweeping preview of his plans to investigate voter fraud in the United States includes those registered in more than one state.

A number of people closest to the president fall into that category, including his Treasury Secretary nominee, Steve Mnuchin; Trump’s son-in-law and close adviser, Jared Kushner; and his younger daughter, Tiffany Trump.

The president tweeted on Wednesday that he will be asking for a “major investigation” into voter fraud, “including those registered to vote in two states, those who are illegal and even, those registered to vote who are dead (and many for a long time),” he said.

“Depending on results, we will strengthen up voting procedures!”

It’s not illegal to be registered in two states and just because someone is, it doesn’t mean they vote in both. Trump’s comments likely suggest a crackdown on those who actually vote in two or more states — claims that secretaries of state across the country have dismissed as baseless.

Mnuchin is registered in New York and California, according to a public voter database, and Kushner in New York and New Jersey. Tiffany Trump is registered in New York and Pennsylvania, where she went to college, according to the database — something presidential counselor Kellyanne Conway called “flatly false.”

“She had been registered in Pennsylvania and went through the process, (and) said it was very byzantine and took a long time, but she said that she is not registered to vote in two states,” Conway said Thursday on NBC’s “Today.”

The president’s chief counsel, Steve Bannon, shifted his Florida registration last summer, from a former home in Miami-Dade County where his ex-wife once lived, to a beachfront home owned by a Breitbart colleague in Sarasota County on the Gulf Coast. On Wednesday, Sarasota Supervisor of Elections Ron Turner told reporters that Bannon never voted in the county and had been removed from the county’s rolls this week based on information received from New York City’s elections office.

A request for comment from the White House on how the proposed investigation might seek to address the two-state registration issue was not immediately answered.

All 50 states and the District of Columbia have finalized their election results with no reports of the kind of widespread fraud that Trump alleges.

Trump has long asserted that the system is “rigged,” but he increasingly vocalized his concerns in August after courts rejected tough voter ID rules put in place for the first time in a presidential election in states including North Carolina, Texas and Wisconsin. The rulings cited a risk of disenfranchising the poor, minorities or young people who were less likely to have acceptable IDs — and who are more likely to vote Democratic.

Trump’s tweet on the investigation alarmed Democrats who already believe that moves to tighten voter ID laws are a means to restrict access to the ballot box. Like the president, Trump’s pick for attorney general, Republican Sen. Jeff Sessions of Alabama, who could oversee any federal probe, has shown sympathy toward claims of voting fraud.

Associated Press writers Jill Colvin and Rhonda Shafner in Washington; Donald Thompson in Sacramento, California; and Terry Spencer in West Palm Beach, Florida, contributed to this report.