South Korea's customs agency is looking into accusations that the youngest daughter of Korean Air Lines' chairman, and other family members, did not pay customs duties on luxury goods brought into the country, the agency said on Wednesday.

Cho Hyun-min, a senior vice president of Korean Air, is already under investigation by police for possible assault after it was reported she threw water at people during a business meeting.

Cho previously told a South Korean TV channel that she "pushed" a cup of water but did not throw it at anyone's face, as media had reported.

Cho, also known as Emily Cho, is the second daughter of the Korean Air chairman to infuriate the public with petulant behaviour.

Her older sister Heather Cho made headlines over a notorious "nut rage" incident in 2014, when she lost her temper over the way she was served nuts in first class and ordered the Korean Air plane return to its gate at a New York airport.

Since the controversy arose surrounding Emily Cho, there have been claims on social media and a local media story citing an unnamed Korean Air employee saying she and other members of the chairman's family bought luxury goods abroad then brought them into South Korea without paying customs tax.

The Korea Customs Service said although the matter is not an official investigation yet, the agency will seek to confirm facts and open an investigation if needed.

Korean Air declined comment.

READ: Korean Air 'nut rage' sister apologises for angry outburst