PUEBLO, Colo. — An FBI manhunt for three heavily armed siblings accused of shooting at a police officer in Florida and robbing a Georgia bank ended Wednesday with a police chase in Colorado, where shots were fired at officers before the suspects’ car rolled and crashed into a guard rail.

The mayhem capped a cross-country search for the two brothers and sister that authorities had warned were armed and extremely dangerous. Police recovered two AK-47 assault rifles and a MAC-11 pistol at the crash site.

“Ladies and gentlemen, I’m proud to say we won,” Pasco County, Fla., Sheriff Chris Nocco said. “We continuously said that if these three fugitives wanted a battle with law enforcement, we would win that battle. And that’s what happened today.”

Ryan Edward Dougherty, 21, and Dylan Dougherty Stanley, 26, were arrested after the 20-mile chase on Interstate 25 that ended in Walsenburg, about 150 miles south of Denver.

Their sister, Lee Grace Dougherty, 29, was shot in the leg after she pointed a gun at a police officer while trying to escape on foot, authorities said.

The manhunt began Aug. 2 in Zephyrhills, Fla., when police Officer Kevin Widner tried to pull over a car for speeding. The occupants of the white Subaru fired at least 20 rounds and shot out the tire of Widner’s patrol car after a five-mile chase at speeds up to 100 mph, authorities said. Widner wasn’t hurt and did not return fire.

Sheriff’s investigators said they linked the siblings to the case when they found Ryan Dougherty’s ankle monitor near the scene of that chase. He had been issued the monitor after being convicted of sending sexually explicit text messages to an 11-year-old girl.

A few hours later and 210 miles to the north, three people wearing masks charged into the Certus Bank in Valdosta, Ga. One waved an AK-47 assault rifle while another carried a machine pistol.

They fired into the ceiling and fled with cash in a white sedan similar to the Subaru in the Florida shooting.

Soon, police posted photos of the siblings on electronic billboards across the Southeast. Citizens reported spotting the car near Forsyth, Ga., and Chattanooga, Tenn. Authorities said they believed the fugitives had put New York tags stolen from Ryan Dougherty’s girlfriend on the Subaru.

“May the Lord look over all of us, because these three are on some type of mission. And it is a violent mission,” declared Sheriff Chris Nocco of Pasco County, Fla.

Police feared the siblings were carrying a small arsenal of weapons. Background checks done by gun sellers showed Ryan Dougherty bought an AK-47 assault rifle — like the one used in the bank robbery — at a pawn shop two years ago. Similar checks showed his brother also owned guns.

Nocco said all three siblings had been living together in Lacoochee, Fla., about 45 miles northeast of Tampa, and each had a criminal record. Lee Dougherty had charges pending against her in Florida for hit and run and had previously been charged with battery, Nocco said, and Dylan Dougherty Stanley had been charged with marijuana possession.

In East Palatka, Fla., the siblings’ mother, Barbara Bell, urged them to surrender last week in an interview with The Associated Press.

“I love all my children very much,” Bell said then. “Although they’ve done some very bad things, no one has been physically injured yet. I would encourage my children to turn themselves in.”

Attention turned West on Tuesday, when the FBI reported the siblings most likely had been spotted at an outdoor goods store in Colorado Springs and could be on their way to a campground or rural area to escape detection. Colorado Springs police said the car now had stolen Texas license plates.

A citizen tipped Colorado state troopers about 9 a.m. Wednesday that the suspects might be at a campground south of Colorado Springs. A Pueblo County sheriff’s detective spotted the car near I-25, followed it discreetly until state troopers joined him, and the chase was on.

AK-47 rounds were fired at the four patrol cars during the chase south on the interstate, where speeds exceeded 100 mph, said Lt. Col. Anthony Padilla of the Colorado State Patrol.

In Walsenburg, troopers deployed spiked stop strips across the interstate. A tire was punctured on the Subaru, sending it rolling and crashing into a guardrail.

The three suspects were treated at a Walsenburg hospital and transferred to Pueblo County Jail.

FBI Special Agent Phil Niedringhaus said the manhunt worked the way one should.

“The key factors here were national media coverage, local media coverage, digital billboards,” he said. “But none of that stuff really makes any difference unless there are citizens willing to pick up the phone and make calls to law enforcement.”

No one could say why the three ended up in Colorado, though Niedringhaus offered his own idea.

“They were here because they were running,” he said.