Sens. Ted Cruz, R-Texas, right, and Josh Hawley, R-Mo., attend the Senate Judiciary Committee markup on judicial nominations and the Online Content Policy Modernization Act, in Dirksen Building on Thursday, December 10, 2020.Tom Williams | CQ-Roll Call, Inc. | Getty ImagesSeven Democratic senators filed a formal complaint Thursday urging the Senate Ethics Committee to investigate GOP Sens. Ted Cruz and Josh Hawley’s efforts to overturn the presidential election results.The complaint comes over two weeks after the deadly Jan. 6 insurrection at the U.S. Capitol led by supporters of former President Donald Trump.”Senators Ted Cruz and Josh Hawley lent legitimacy to President Trump’s false statements about election fraud by announcing that they would object to the certification of electors on January 6,” the senators wrote in a letter to Senate Ethics Committee leaders Chris Coons, D-Del., and James Lankford, R-Okla.Cruz, a Republican from Texas, signed a written objection to certifying Arizona’s votes toward the beginning of the joint session to count electoral votes on Jan. 6, prompting a debate in both chambers. Then, pro-Trump rioters stormed the U.S. Capitol building and lawmakers evacuated.After the Capitol was secured and lawmakers resumed the session, Cruz and Hawley along with other Senate Republicans voted against Arizona’s Electoral College results, even as others who had planned to object decided to vote for the certification following the deadly attack.Hawley, of Missouri, also continued with his previously announced plan to sign a written objection to Pennsylvania’s electoral votes. Cruz and Hawley voted against accepting Pennsylvania’s election results.”By proceeding with their objections to the electors after the violent attack, Senators Cruz and Hawley lent legitimacy to the mob’s cause and made future violence more likely,” the senators said in the letter.The letter is signed by Sens. Sheldon Whitehouse of Rhode Island, Ron Wyden of Oregon, Tina Smith of Minnesota, Richard Blumenthal of Connecticut, Mazie Hirono of Hawaii, Tim Kaine of Virginia and Sherrod Brown of Ohio.In the letter, the senators ask Coons and Lankford to investigate whether the actions of Cruz and Hawley constitute “improper conduct” or otherwise violate the Senate code of ethics.The offices of Cruz, Hawley, Coons and Lankford did not immediately respond to CNBC’s request for comment.In the wake of the Capitol insurrection, Cruz and Hawley issued statements condemning the violence.”The attack at the Capitol was a despicable act of terrorism and a shocking assault on our democratic system,” Cruz said in a press release Jan. 7.”These acts of violence were criminal. They must be condemned,” Hawley said in a statement Jan. 8.Hawley received criticism after he was seen saluting protestors outside the Capitol with a raised fist before the joint session began. Publisher Simon & Schuster announced Jan. 7 it would no longer publish Hawley’s forthcoming book, though the senator has since found a new publisher.Trump faces a second impeachment trial in the Senate, even though he is now out of office. The Democratic-controlled House impeached Trump on Jan. 13 for inciting the Capitol insurrection.Lawmakers have also requested other investigations of the riot. The Democrat-led House on Jan. 16 sent a letter to FBI Director Chris Wray and other agency chiefs seeking information on the intelligence and security failures that led up to the breach of the U.S. Capitol. On Thursday, House Oversight Chairwoman Carolyn Maloney, D-N.Y., asked Wray to look into the role that social media site Parler played in the attack.Five people lost their lives as a result of the insurrection, including a U.S. Capitol police officer.