Some out-of-state witnesses in the case have gone to court to challenge subpoenas or other legal testimony they seek to testify. But after Mr. Giuliani failed to appear at a hearing last week in Manhattan where the matter was to be heard, Fulton County Superior Court Judge Robert CI McBurney ordered him to appear before a special grand jury in Atlanta in August. 9. Mr. Giuliani, who spearheaded efforts to keep Mr. Trump in office as his personal lawyer, has emerged as a central figure in Georgia’s criminal investigation into efforts to overturn Mr. Trump’s 2020 election loss in the state. Fani T. Willis, the Fulton County district attorney leading the investigation, has indicated she is considering conspiracy or racketeering charges, which could be brought against a wide range of people involved in multiple efforts to influence election results. Her office worked with the office of Alvin Bragg, the Manhattan district attorney, to secure Mr. Giuliani’s testimony, and she said in a statement that she was “grateful to the prosecutors and investigators” in Mr. Bragg’s office for their help. A lawyer for Mr. Giuliani did not immediately respond to a request for comment. A special grand jury convenes regularly in Atlanta to hear testimony and review documents and videos that may shed light on the multifaceted effort to put Georgia in Mr. Trump’s victory column. Among the actions under scrutiny is an infamous post-election phone call Mr. Trump made to Brad Raffensperger, the Georgia secretary of state, asking to “find” enough votes to ensure his victory. Mr. Giuliani appears to be of interest for a number of reasons, including his involvement in a plan to frame pro-Trump presidential electors in several states, including Georgia. In court filings this week, it was revealed that all 16 pro-Trump voters in Georgia had been told by the Fulton County District Attorney’s office that they could face charges. Mr. Giuliani also appeared in person before two Georgia state legislative committees in December 2020, where he spent hours peddling false conspiracy theories about secret Democratic ballot bags and damaged voting machines. He told state lawmakers, “You can’t certify Georgia in good faith.” Legal experts said the Georgia probe could prove particularly dangerous for Mr. Trump and his allies. Although the grand jury process is secret, some details have emerged in recent days that hint at the scope of the investigation. Among the pro-Trump voters who learned they could be indicted are David Shaffer, the state Republican Party chairman, and State Sen. Bert Jones, the party’s nominee for lieutenant governor. Another Republican senator, Brandon Beach, has also been tipped as a possible target. Prosecutors are seeking testimony from Senator Lindsey Graham, a Trump ally who also called Mr. Raffensperger, and Representative Jody Hice, a far-right Georgia Republican who has embraced false narratives of voter fraud in Georgia and who helped lead the effort. in Congress to keep Mr. Trump in power. William K. Rashbaum and Jonah E. Bromwich contributed reporting.