A scuffle broke out at an amusement park in Westchester County on Tuesday when a group of Muslims there to celebrate the end of Ramadan were told that women could not wear their head coverings on certain rides, park officials and witnesses said. Fifteen people were arrested. 

The Muslim American Society of New York had arranged the trip to Playland Park in Rye, which was expected to bring some 3,000 people to the site from New York City, as well as surrounding suburbs like Yonkers and parts of Long Island. 

About 2:30 p.m., the day took a sour turn when some of the female Muslim visitors, most of whom arrived in head scarves, were told they could not get on certain rides — including the Catch-a-Wave ride, the Crazy Mouse roller coaster and the Dragon Coaster — because their heads were covered by the Muslim hijab. 

Ola Salem, 17, of Coney Island, Brooklyn, was visiting with the group to celebrate the Muslim holiday of Eif ul-Fitr, or the end of the holy month of Ramadan, and wearing a pink and gray head scarf. She said she asked a park employee if she could join her 8-year-old sister on a ride. 

“They said no because of my ‘headgear,’ “Ms. Salem said. “I said, ‘It’s not my headgear, it’s my religion.’” 

Ms. Salem said she asked to speak with a supervisor and was presented with a list of rides that would require her to remove her scarf. More than a dozen of the park’s rides, she said, were on the list. 

“It got heated,” said Kathleen M. O’Connor, commissioner of the Westchester County Parks Department. “They were frustrated they couldn’t get on the rides.” 

According to park officials, disappointed customers were then offered a refund, and several people proceeded to the park’s main entrance to get back the $20 each member of the group had paid. 

Then, the Parks Department said, about 20 members of the Muslim American group started fighting among themselves. Peter Tartaglia, the deputy commissioner of the department, said there was pushing and shoving, so some park rangers intervened. One ranger sustained an injured shoulder; another injured a knee. 

Fifteen people, men and women, were placed under arrest, county officials said, though they did not specify whether all of them were members of the tour group. They were charged, the officials said, but the charges were not specified, and all of the arrested were released. 

Some people who came to the park with the group said the fight began when a park employee touched a Muslim woman, at which point tempers flared. 

“We don’t have any knowledge of that at all from the police end or from the parks end,” Mr. Tartaglia said. 

County officials blamed the trip’s organizers for not informing the guests that they would have to remove their headscarves. 

Playland Park, owned and operated by the county, has come under scrutiny in recent years after three people died there from 2004 to 2007, including a 7-year-old girl who was killed on a ride called the Mind Scrambler. 

County officials say that the ban on headgear for some rides is a longstanding safety policy and that the organizers had been warned about it. “We told them several times we have what we call a headgear policy, meaning there are certain rides where you can’t wear headgear of any sorts,” Mr. Tartaglia said. He said he was not aware of specific instances where headscarves had caused injuries. 

“Something flying off your head could land on the track” and require a ride to be stopped, he said. He added, “If you have a scarf on, you could be choked.” 

Sharif Aly, vice president of the Muslim American Society of New York, said that the organization planned to investigate what happened before drawing any conclusions.