Manchester, New Hampshire — Former President Donald Trump's closing message to New Hampshire voters contains falsehoods about the upcoming primary election, including a baseless claim that Democrats are planning to "infiltrate" the primary to support former South Carolina Gov. Nikki Haley. 

"Nikki Haley is counting on Democrats and liberals to infiltrate your Republican primary," Trump said to a small ballroom filled with supporters in Portsmouth Wednesday evening, before blaming New Hampshire Gov. Chris Sununu for the state's primary system, which allows undeclared voters — which make up 40% of the state's registered voters — to vote in either the Republican or Democratic primary on Jan. 23. 

Trump repeated the same unfounded claims to a crowd of over 1,000 in Atkinson, New Hampshire, Tuesday night, and inaccurately stated that Democrats want to "cancel out" votes for him.

By law, undeclared residents may vote in New Hampshire's GOP primary, along with Republican voters. Registered voters may only vote in one party's primary, and the deadline to switch party registration expired in early October.

Of the state's more than 873,000 registered voters, just 3,542 voters changed their registration from Democrat to undeclared before the state's Oct. 6 deadline, and just 408 Democrats changed their registration to Republican.

The electorate in New Hampshire is more moderate than in Iowa, where Trump cruised to a decisive victory in this week's caucuses, giving Haley a lane to challenge Trump in the Granite State if she can court enough moderate or independent support.

"I think Trump is one hundred percent correct to have a concern with left-leaning people voting in the Republican primary, but I think Donald Trump will be winning New Hampshire by a significant amount," one Republican New Hampshire political strategist told CBS News. "And I don't think enough people will that are left-leaning will overcome the amount of supporters you have in the state of New Hampshire."

Trump's rhetoric in New Hampshire is the latest example of his embrace of falsehoods and mis- and disinformation surrounding voting in the U.S., as he continues to claim that the 2020 election was "stolen" from him. 

"President Trump is absolutely correct when he says Nikki Haley is relying on liberals and Democrats to infiltrate because that's who she appeals to," Trump campaign spokesperson Steven Cheung told CBS News. 

The former president has also promised Granite Staters he'll help the state that he once called a "drug-infested den" by lowering energy costs, taking care of both New Hampshire's fishing and large veteran communities. 

"You inherit the legacy of red-blooded New Hampshire patriots and you really are incredible patriots who lived by that immortal motto 'Live Free or Die,'" Trump said in Portsmouth. "That's pretty cool. Well, we'll get it done without the dying part, but, you know, we don't want the dying part. But if you're willing to do that, if you have to."

— Kabir Khanna and Olivia Rinaldi contributed to this report.