Texas is asserting its sovereign immunity against Congress, telling Democrats on two congressional committees this week that the state has no obligation to comply with their investigative demands.

Attorney General Ken Paxton’s office says that as a state with sovereign powers under the Constitution, Texas can’t be treated like a federal agency or Cabinet secretary who can be compelled to comply.

“Texas does not draw its authority from the United States or the United States Constitution, but from its status as a dual sovereign within the union,” Jeffrey C. Mateer, first assistant attorney general, wrote in a letter Monday to the House Oversight and Reform Committee.

Mr. Mateer fired off a similar letter Wednesday to the House Ways and Means Committee rebuffing its attempts, saying the state wouldn’t stand to be treated like a “subdivision of the federal government or a private citizen.”

“Granting Congress the power to exercise ‘oversight’ over the constitutional officers of a state engaged in the lawful exercise of that state’s core authority would undermine the fabric of our system of dual sovereignty,” Mr. Mateer wrote.

The defiance in some ways tracks that of President Trump, who has said House Democrats’ investigations into the president’s business, family and myriad official actions are harassment.

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Texas is objecting to Democrats’ requests for documents probing the state’s efforts to clean up its voter rolls, and documents detailing the state’s efforts to protect faith-based adoption and foster care providers against an Obama-era rule about working with same-sex couples.

The clash could break new legal ground.

Ken Cuccinelli, a former Republican attorney general in Virginia, said he never encountered the situation during his time in office, but he added that two constitutional principles are at stake: the sovereignty of states and the supremacy clause, which gives the federal government an edge in clashes with states.

He said Texas makes a strong case in its letters for why it will prevail.

“Congress doesn’t get to do oversight over states — period. Nor can they compel action by state officers,” he said. “If I were a betting man, I’d take Texas and give two touchdowns on this one.”

Josh Blackman, a professor at the South Texas College of Law in Houston, said the House committees have issued requests only for documents. Things will get more complicated if either committee feels strongly enough to approve subpoenas.

Mr. Blackman said Texas could try to head that off by suing first, picking a court in Texas and asking for a temporary restraining order against having to turn over any documents while the state argues its case that its officers aren’t subject to federal demands.

He said prior Supreme Court cases have held that Congress can’t “commandeer” a state to enact laws, nor can it force state officials to perform tasks such as run background checks on firearms purchases.

“I usually think of commandeering in the context of legislation, but I don’t see any reason why you have to limit it to legislation,” he said. “It’s [that] Congress can’t give orders pursuant to legislative powers to tell states what to do.”

Neither the oversight nor Ways and Means committee responded to requests for comment on Texas’ challenge, nor did the office of Rep. Jamie Raskin, the Maryland Democrat who chairs an oversight subcommittee looking into the voting issue.

After a previous exchange, though, the oversight committee brushed aside Texas’ claims of sovereignty and insisted that the information would eventually be turned over.

Investigating the states is not new to Congress.

In recent years, the House Oversight and Government Reform Committee investigated the drinking water problem in Flint, Michigan, sparring with then-Gov. Rick Snyder over access to state documents.

It also investigated Oregon’s implementation of its Obamacare website, finding enough fault to ask for criminal charges to be brought against state officials.

In these new cases, the oversight committee is probing Texas’ announcement this year that it found some 95,000 names on voter rolls it suspected of being noncitizens. The state moved to begin to purge the names, drawing a lawsuit from Hispanic and voters rights groups. The sides reached a settlement last month.

The Ways and Means investigation, meanwhile, deals with a request Texas made last year to the federal Health and Human Services Department asking to be freed from Obama-era rules denying assistance to states that certify faith-based adoption or foster parent organizations that won’t work with same-sex couples.

Mr. Mateer, in his letters, said the committees are entitled to ask federal agencies for information they have, including communications with Texas. He also said they are entitled to any documents from Texas that a citizen would be able to get through the state’s open records laws.

The Texas attorney general’s office also questioned the validity of the committees’ inquiries, saying they haven’t identified a valid legislative purpose. The Supreme Court has held that while Capitol Hill has broad investigative powers, they must be tethered to some lawmaking, either now or with the prospect of legislating.

That is the same argument the Trump administration made this week in objecting to the expansive document demands from the House Judiciary Committee, which is looking to redo and expand on the special counsel’s report into the 2016 election and Russian meddling.

In the case of the voting inquiry, Mr. Mateer said there is no right for noncitizens to vote, so there is nothing Congress could legislate over.