Amestoy said investigators believe the woman, whose identity had not been determined Monday, killed herself with a .22-caliber sawed-off rifle. She also fired but did not hit the deputy, he said.
A third woman, Robin Collins, 43, was arrested and handcuffed by Robinson moments before the shootout, Amestoy said. She was being held Monday night pending extradition to Colorado, where she is wanted for burglary.
Carpenter, 32, sent shockwaves through Clear Spring in August when residents learned he did not return from an unsupervised weekend pass from the Patuxent Institution Re-Entry Facility in Baltimore.
FBI Special Agent Barry O'Neill said his agency was informed of Carpenter's death Monday because there was a federal warrant on file charging him with unlawful flight.
When he was 17, Carpenter was convicted in the 1982 murder of his grandmother. Tried as an adult, he got a life sentence the following year.
In the days following his escape, Maryland State Police and the Washington County Sheriff's Department investigated several reports that he had been spotted but never found him.
Robinson, who was released from the hospital on Sunday, investigated reports on Friday morning that three people were painting a rented U-Haul truck in a campground, Amestoy said. Later in the afternoon, Robinson pulled over the truck, which was driven by Collins.
After arresting Collins, Robinson flagged down a vehicle that was lagging behind, Amestoy said. The car pulled in front of the U-Haul and Carpenter and the woman jumped out.
"They came out shooting," Amestoy said.
The deputy had been on the job for five days, Amestoy said.
Montana authorities seized both vehicles following the shooting. Amestoy said the vehicles contained numerous items that investigators believe may have been stolen.
The relationship among Carpenter and the two women was unclear, but Amestoy said authorities believe the two women knew each other in Colorado Springs, Colo. He said investigators believe Carpenter was traveling with the unidentified woman and picked up Collins in the Midwest.
Amestoy also said officials have contacted authorities in Minnesota because they believe the trio may have been responsible for an armed robbery there.
The shooting of a law enforcement officer is nearly unheard of in Phillips County, a 5,000-square-mile area of about 5,000 residents. Amestoy said vast portions of the county are unpopulated and more than half live in Malta, the county seat 60 miles from the site of the shooting.
Amestoy said officials could not remember the last time a law enforcement official fired his gun in the line of duty in Phillips County, which is nearly 11 times the size of Washington County with 25 times fewer residents.
At the time of his escape, Carpenter was serving a life sentence for the 1982 shooting death of his grandmother.
After shooting his grandmother, Carpenter fled to New York State and was returned to Clear Spring by relatives, court records showed.
He then led police to the body of 77-year-old Vada Viola Carpenter, found wrapped in bedclothes and covered with cedar branches near the C&O Canal National Park on Dec. 5, 1982.
She had been shot once at close range with a shotgun as she lay sleeping on Nov. 28, court records said.
The Associated Press contributed to this story.