A group shook the iron security gate at the property entrance until a door to the gate opened, the video shows.
“The governor (Jay Inslee) was never in danger,” Washington State Patrol Sgt. Darren Wright said at a news briefing.
Inslee did not immediately comment on the breach.
Trump had urged his supporters to fight against the ceremonial counting of the electoral votes that will confirm President-elect Joe Biden’s win.
Many of the protesters in Olympia wore Trump clothing, but also told KIRO they were there to complain about the state’s pandemic restrictions.
The state patrol made no arrests.
“If you make one arrest, that could agitate the crowd and make things worse,” Wright said. “If they’re not creating violence at the moment and they’re not destroying property, we have time on our hands, and we want to try to keep it as peaceful as possible.”
Protesters left peacefully after additional troopers and sheriff’s deputies arrived at the property. Wright says they know of no damage to the grounds other than the front gate.
Protests in several state capitals
As demonstrators rioted in Washington, D.C., there were smaller and more subdued pro-Trump protests in state capitals and other cities.
Protesters at a “Stop the Steal” rally at Arizona’s historic State Capitol in Phoenix caused some damage to the building. A photo taken by a staffer with the Arizona Republic newspaper showed a cracked window on the door to the Capitol entrance, which was closed.
The building has served only as a museum for many years. The actual offices and chambers of state government are located in other buildings nearby.
Department of Public Safety spokesman Bart Graves said, “There has been some minor damage but no arrests have been made.” He did not provide details about the damage.
Later, demonstrators who had marched separately to the Capitol were ordered to disperse because they were participating in an unlawful assembly.
At least one person was arrested after the gathering was declared an unlawful assembly. “One arrest for harassment & disorderly conduct,” Oregon State Police said in a tweet.
In Atlanta, dozens of people stood across from the Capitol, many holding flags. In Denver, hundreds of people gathered outside the Colorado Capitol.
Authorities say a pro-Trump protest inside the Kansas State Capitol in Topeka was peaceful. “There are no known issues that I am aware of,” Lt. Terry Golightly, a spokesperson for Kansas Capitol Police, told CNN. The demonstration was permitted for an hour and had ended, he said.
Some state employees in Utah were allowed to leave work three hours early due to security concerns about a “Stop the Steal” rally outside the Capitol.
“Workers were given the option of early work release,” Sgt. Nick Street with the Utah Highway Patrol said, adding the Capitol was never evacuated.
Street says there was no serious violence at the event — only a minor altercation between a protester and a possible counterprotester.
CNN’s Christina Zdanowicz contributed to this report.