The pair shimmied up a ledge and entered through a second-floor window June 15, patrol spokesman Bob Calkins told The Olympian.
They took a Squaxin Island Tribe blanket, a Native American mask, a bottle of wine and a ceremonial state patrol hat, he said. Other high-value items, including computers and cameras, were left alone.
"We don't think they knew it was the governor's office," Calkins said.
One of the suspects, Emily Huntzicker, 22, of Beaverton, Oregon, was arrested for investigation of second-degree burglary Monday night after patrol Sgt. Matt Wood pulled over her Subaru on Interstate 5 in Chehalis.
He noticed the ceremonial hat for troopers inside and found the bottle of wine - empty - on the floor, Calkins said.
Huntzicker made an initial appearance in Thurston County Superior Court on Tuesday and was scheduled for an arraignment July 8. She was ordered not to leave the state before then.
Huntzicker told a detective she and her friend entered the governor's office through an open window and "just started taking stuff," court papers said. Efforts by The Associated Press to reach her were unsuccessful.
Calkins said the other suspect was arrested Tuesday and she was expected to make a court appearance Wednesday.
The patrol is investigating whether the window was left unlocked. The burglary was discovered the next morning when a state patrol cadet noticed the hat was missing and quickly reviewed surveillance video of two women entering through the window.
The patrol did not publicize the June 15 burglary because authorities did not want to alert the suspects and give them the opportunity to destroy evidence, Calkins said.
Inslee's spokesman, David Postman, said his boss was aware of the burglary, but "it's nothing that's shook anyone here."
"It's certainly disconcerting that this could happen at all," Calkins said.