NEW YORK (CBSNewYork.com) – You are now free to move about the country.

Unless you show too much cleavage?

So says a woman named Avital.

Avital was boarding a 6 a.m. Southwest Airlines flight on June 5 from Las Vegas to New York, wearing a cotton black dress, flannel shirt and scarf.

Avital claims she was politely chatting with an airline worker – who then told her cleavage was inappropriate and that she wouldn’t be able to board the flight unless she buttoned up her flannel shirt.

“I was stunned more than anything,” Avital told CBSNewYork. “We had been chatting about the experience of being up and awake at 4:30 a.m., and then her tone changed quite suddenly. It wasn’t until I walked away from the check-in counter that her words made an impact. Then I got indignant and self-conscious.”

Avital declined to cover up and boarded the plane — cleavage and all. The flight and Avital apparently made it to New York without incident.

“[I didn’t] think there was anything that special about the outfit I was wearing. It had topped 115 degrees in Las Vegas when I was there, and most people were scantily dressed just to stay cool. I hadn’t even considered that it would have been a big deal,” Avital said.

She added that she “most likely” will not be flying Southwest again.

“I initially chose [Southwest] because they were by far the cheapest option. However, if the hidden cost is that I or other passengers will be shamed or judged without official policy to back it up, then it’s not worth it.”

“If Southwest wants to impose a dress code, they are entirely within their rights as a private company. If they would like to ask all of their customers to wear big blue sunhats, that’s their business. What bothered me was not knowing what might set off an individual employee, who could prevent me from boarding based on their personal opinions,” Avital said.

Southwest spokesperson Christi McNeill told Jezebel, who first reported the story, the airline offered Avital an apology and a refund “as a gesture of goodwill,” but that their Contract of Carriage allows them to refuse to transport a customer whose clothing is lewd, obscene, or patently offensive.

According to Avital, she wasn’t looking for any fashion awards with her outfit – just to be comfortable.

“I was by no means fashion plate of the century with that get-up, but I wasn’t trying to be,” she said. “I was just trying to board quickly and safely, and catch up on my sleep in-flight — just like everybody else.”

This isn’t the first time Southwest has made headlines or has had to apologize over its policies.

In May 2011, Kenlie Tiggeman, a 30-year-old political strategist and weight loss blogger in New York City, said she and her mother were told by a Southwest gate agent that they each had to buy two seats and that it was humiliating — being told she was too fat to fly.

“It was rude. It was in front of lots of people,” Tiggeman, who’s originally from New Orleans, told CBS 2’s John Slattery.

“And said that we were, in fact, too fat to fly, without an additional ticket,” Tiggeman said.

Yet, this was a return flight, and they hadn’t been stopped before. The gate agent said it was policy.

“I was asked what size clothes, and how much I weigh. I gave answers in front of a gate full of people, some of whom were snickering,” Tiggeman said.

A spokeswoman for Southwest said: “If a passenger cannot fit in a seat with the armrests down, a second seat must be purchased. If the flight is not full, that added charge will be refunded.”

But Tiggeman said she does fit in a seat.

Southwest, which allowed the woman and her mother on a later flight, apologized, refunded their tickets and gave them free vouchers.

What do you think? Do you think Southwest should have a say in how passengers dress for flights? Did they go too far? Sound off below.