WASHINGTON (REUTERS) - Two women were arrested in Florida for running two security checkpoints near Mar-a-Lago on Friday (Jan 31) in a police car chase that was unrelated to US President Donald Trump's resort, officials said.

Trump was in Washington at the time, but was scheduled to leave for his Palm Beach resort later on Friday.

The vehicle's driver, identified as Hannah Roemhild, 30, initially attracted police's attention for dancing on top of a car, Palm Beach County Sheriff Ric Bradshaw told reporters.

A car chase ensued through the town of Palm Beach with speeds in excess of 70mph (110kmh) and Roemhild driving her black SUV on the wrong side of the road at times, he said.

"This is not a terrorist thing," Bradshaw told a press conference, adding that Roemhild did not appear to have a police record and had a Connecticut driving licence.

"This is someone who was obviously impaired somehow and driving very recklessly."

Officers fired on the vehicle after it crashed through two checkpoints and approached a third at about 11.40am EST (12.40am on Saturday, Singapore time), the sheriff's office said.

Roemhild is likely to face charges of assault on a federal officer, deadly assault on a sheriff's deputy and various traffic charges for driving her car through the checkpoints, Bradshaw said.

Nobody was injured, he said.

The two were taken into custody after the Florida Highway Patrol, which had been pursuing the SUV, continued the chase along with a sheriff's helicopter, the sheriff's office said.

"There was clearly no intention," said Bradshaw.

"I'm not so sure she knew where she was going."