Conway, who is accused of repeatedly violated the 1939 Hatch Act that limits political activity by government workers, did not attend a hearing on Wednesday, prompting the Democratic-led panel to vote 25-16 to issue the document.
The hearing was scheduled after the Office of Special Counsel, a US government watchdog agency, earlier this month recommended Conway be fired for disparaging Democratic presidential candidates while speaking in her official capacity during television interviews and on social media.
The White House has said it would not allow Conway to appear for the questioning.
“In accordance with long-standing precedent, we respectfully decline the invitation to make Ms Conway available for testimony before the Committee,” White House legal counsel Pat Cipollone told Democratic Representative Elijah Cummings, the panel’s chairman, in a letter on Monday.
Republicans accuse Democrats of trying to curb Conway’s free speech.
Career government officials found to have violated the Hatch Act can be fired, suspended or demoted, and fined up to $1,000.
The president, vice president and certain other senior officials are exempted.
Cummings said on Wednesday that Conway’s actions were a clear-cut violation of the law and President Donald Trump should fire her.
Trump has said he would not fire Conway, 52, a former political pollster who became Trump’s campaign manager in 2016 and the first woman to oversee a winning US presidential campaign.
The president has praised her for her “success” in her career.
House Democrats have been frustrated by the Trump administration’s stonewalling of their efforts to hold senior officials to account.
Treasury Secretary Steven Mnuchin, Commerce Secretary Wilbur Ross, Attorney General William Barr and other officials have defied subpoena requests from Democratic-led House panels in recent months.