Gwinnett County police Monday identified the woman allegedly shot in the abdomen by Clayton County Sheriff Victor Hill as Gwenevere McCord, 43, of Jonesboro.

McCord, a Paran Realty agent who worked inside the 3,800-square-foot, Lawrenceville-area model home where the shooting happened Sunday, remained in critical condition Monday at Gwinnett Medical Center.

“She’s not able to give any information due to her condition,” police Sgt. Brian Doan said.

McCord and Hill, who are acquaintances, were the only two people inside the home on Britt Trail Drive when the shooting happened, police said. However, other witnesses in the subdivision have been interviewed, according to Cpl. Deon Washington, who said Hill called 911 at 5:39 p.m. Sunday to report the shooting.

But when officers arrived at the shooting scene, Gwinnett police said Hill “refused to cooperate and give any statement.” By noon Monday, Gwinnett police said Hill still had not made a statement to investigators.

Despite his refusal to answer questions from investigators, police allowed Hill to leave the scene on his own. According to Georgia law, “a sitting sheriff cannot be charged except by a warrant issued by a Superior Court judge,” Gwinnett County District Attorney Danny Porter said Monday in an interview with AM750 and 95.5 FM News/Talk WSB, a news partner of The Atlanta Journal-Constitution.

“You have to have the warrant issued before the sheriff can be arrested,” Porter said. “What I’m trying to figure out is, does that apply to a sheriff all the time, or only in the performance of his official duty.”

He said police Monday were trying to reconstruct the incident, “which is a little more difficult because Sheriff Hill declined to give a statement yesterday.”

Once police determine how the shooting took place, “then we’ll make a decision on what, if any, appropriate charges there are,” Porter told WSB.

Asked how long that might take, Porter said, “police should have their investigation wrapped up fairly quickly, and then we’ll have a decision in the next few days.”

Gov. Nathan Deal said Monday that it was too early for him to comment on whether he will take action against Hill.

“I only know what I’ve read in the newspaper and heard on the radio,” Deal said. “It’s very premature. I do not have the ability to remove anybody — sheriff or otherwise — at least until he’s indicted. He has not been indicted, and whether or not he will be is a question that remains to be seen. If and when that happens, we’ll follow the course and the process that the law allows.”

Officers executed a search warrant and remained at the scene of the shooting for several hours Sunday. The weapon used was located inside the home, but it was not known if it was Hill’s county-issued gun.

It was also not known how the incident may affect Hill’s job. Clayton Commission Chairman Jeff Turner said the governor is the only one who could remove Hill from office.

“We have to see how the situation unfolds,” Turner said Sunday night. “He’s still the sheriff of this county. We just have to put our faith in the justice system and see what develops and handle it accordingly.”

Janice Dean was visiting a relative in the Park Haven subdivision just a few houses down from the model home when the shooting happened.

“It’s a long way to come to shoot someone accidentally,” Dean said. “I would expect him to have a gun in Clayton County, absolutely. But once he’s not in Clayton County, it should stay in the car.”

The shooting comes less than three weeks after the former Peachtree City police chief was indicted for allegedly shooting his former wife on New Year’s Day. On April 15, a Fayette County grand jury indicted William McCollom on a reckless conduct charge for the shooting, which paralyzed Maggie McCollom.

Hill, 50, is in his second term as sheriff and began his current term Jan. 1, 2013. He was also sheriff from January 2005 through 2008. Both of terms in office have included controversy.

In 2013, Hill was acquitted of racketeering charges related to his use of a county-issued credit card.

During the final week of his first term, Hill filed for bankruptcy, due partly to the amount of money he owed in damages for lawsuits against him. On his first day in office in 2005, Hill fired 27 deputies, who later sued for wrongful termination. They won their jobs back and settled for $7 million, which was paid by Clayton County.

— Staff writers Greg Bluestein, Arielle Kass, Tammy Joyner and Christian Boone contributed to this report.