A Georgia district attorney’s request to convene a special grand jury was approved Monday in the criminal investigation into former President Donald J. Trump’s attempts to overturn the 2020 election results in the state.

Fani T. Willis, an Atlanta prosecutor, requested the grand jury last week after crucial witnesses identified by investigators refused to cooperate voluntarily. A grand jury — which could issue subpoenas — is the next step in an inquiry that legal experts see as potentially threatening for the former president.

“The special purpose grand jury shall be authorized to investigate any and all facts and circumstances relating directly or indirectly to alleged violations of the laws of the State of Georgia,” stated the approval order, signed by Christopher S. Brasher, the chief judge of the Fulton County Superior Court.

The grand jury would start its work on May 2 and continue “for a period not to exceed 12 months,” the order said.

Legal experts have been watching the Georgia case for months, and say the former president’s criminal exposure could include charges of racketeering or conspiracy. It is the only known criminal case that focuses directly on Mr. Trump’s efforts to overturn the election.

Politically, the case takes place in a state that played a pivotal role in President Biden’s path to the White House. Mr. Biden became the first Democrat since 1992 to win Georgia’s electoral votes in 2020. The two-month period that followed his victory has been the focus of Ms. Willis’s criminal investigation.

After Mr. Trump’s election loss — and before Georgia held two Senate elections in January — Mr. Trump began to publicly dispute the results of the election in states he lost, including Georgia. On Jan. 2, he called Brad Raffensperger, Georgia’s secretary of state, and asked him to “find 11,780 votes” — the margin by which Mr. Trump lost the state.

The call kicked off a firestorm that continues to have political and legal ramifications. Mr. Trump, who remains the most influential figure in Republican Party politics and is a likely candidate for president in 2024, has previously stated that his call with Mr. Raffensperger was “perfect.”