Maine State Police say the man who accidentally shot a 22-year-old woman in the head Monday afternoon in Bath was the woman’s boyfriend.

Chelsea Jones of Thomaston remained in critical condition Tuesday night at Maine Medical Center in Portland following the shooting in the Shaw’s supermarket parking lot just before 4 p.m. Monday.

The woman’s boyfriend, Dylan Grubbs, 23, of Thomaston, has been cooperating with the investigation, state police spokesman Stephen McCausland said.

Grubbs had driven to the parking lot to meet a man interested in buying the handgun. Jones was sitting in the front seat of the sport utility vehicle – and Grubbs was showing the pistol to the prospective buyer outside the vehicle – when the gun went off, McCausland said.

Police are still trying to determine exactly what was happening when the gun went off and will probably have to interview Grubbs again, McCausland said.

The prospective buyer was not identified by police because he is a witness in the case, McCausland said. There appears to be nothing inappropriate in the planned sale, he said.

“The sale and purchase of the gun itself doesn’t seem to raise any red flags,” he said.

Grubbs has a prior criminal history that includes a misdemeanor assault in 2014, drunken driving in 2013 and criminal threatening with a dangerous weapon, a felony, in 2006, when he was 14. Normally, a felony would disqualify someone from owning a gun but certain juvenile convictions are no longer disqualifying after the person turns 18.

The gun has been taken to the Maine State Police crime lab in Augusta for analysis. McCausland would not release the make and caliber of the handgun.

Maine Moms Demand Action, a group working to get a statewide referendum to mandate background checks in most private gun sales, said the case shows how many gun sales are carried out between “strangers meeting in public places to transfer a weapon, no questions asked.”

“There is a flourishing, unregulated market for unlicensed gun sales that take place in supermarket parking lots, near places kids play – virtually anywhere,” said Dallas Denery, a volunteer with the group from Bath. If successful, the group would have a referendum on next fall’s ballot seeking to require sales at gun shows and between individuals to include a background check by a federally licensed gun dealer.

Todd Tolhurst, president of Gun Owners of Maine, said Monday’s shooting has nothing to do with background checks.

“This was an accident that happened through negligence or ignorance,” Tolhurst said. “People make mistakes and use bad judgment. No amount of universal background check would change that.”

Tolhurst said that even if all sales required a federally licensed gun dealer to conduct a background check on the buyer, sellers and buyers will still meet beforehand to determine whether they want to make the purchase.

The circumstances of Monday’s shooting remain under investigation by Bath police.