Scott Gordon, NBC 5 News
The woman told Jezebel.com that an airline employee told her she wouldn't be able to board her flight unless she covered up her cleavage.
Southwest Airlines has apologized to a passenger who claims an airline employee told her she couldn't fly unless she covered up her cleavage.
"We reached out to apologize and offered a refund as a gesture of goodwill," the airline said in a statement. "Regarding our policies, each situation is very different."
The woman -- identified only by her first name Avital -- told Jezebel.com that she was on a flight from Las Vegas to New York on June 5 when the incident happened.
An airline employee at a ticket kiosk told her she'd have to cover up her cleavage or she would not be allowed on the flight, she said.
The woman said she proceeded to the gate without covering up and nobody said anything further.
A photo of the woman obtained by Jezebel.com showed her dressed in a low-cut dress, a flannel shirt and a scarf.
Most passengers at Dallas Love Field said they had no problem with how the woman in the picture was dressed.
"I think she looks great," one woman said. "I mean, nothing's popping out."
In its statement, Dallas-based Southwest Airlines said each case is treated differently.
"Our employees are responsible for the safety and comfort of everyone on board the flight," the airline said. "We do our best to promote a family-centric environment, and we count on our customers to use good judgment and exercise discretion while traveling."