The Coast Guard is investigating a parasailing accident off Ala Moana Beach Park that injured a family of three yesterday.

The parents and their pre-teen daughter were in a harness and flying in a parasail about 8:30 a.m. when a tow line broke and the family fell into the water.

The vessel turned around, picked up the family, and took them back to Kewalo Basin.

Paramedics took a 36-year-old man, a 32-year-old woman, and an 8-year-old girl to the hospital, all in serious condition, an Emergency Medical Services supervisor said.

Mark Neumann, owner of Hawaiian Parasail, said it was his company’s first serious accident in 34 years of operation. He said the weather conditions were not dangerous for parasailing, but an unusually fast squall swept in.

“That squall came really fast, and it was hard to avoid,” he said. “It brought with it very powerful winds, and that’s why the line broke.”

He said the line, 29 days old, was built to hold 8,000 pounds.

After the family fell into the water, the parachute was still inflated and dragged them backwards.

Neumann visited the family in the hospital and said the woman had swelling to her cheek from hitting the boat during her rescue and the man had soreness in his neck. The girl was shaken up, but seemed OK, he said.

He said the Coast Guard ordered drug testing for the captain as part of the investigation, and the company canceled the rest of its tours yesterday out of respect for the family.