Cho Yang-ho, 69, and his brothers and a sister allegedly avoided paying 50bn won ($45mn) in taxes on the overseas assets they inherited after their father Cho Choong-hoon died in 2002.
The matriarch of the troubled Korean Air dynasty was grilled Monday over allegations she used company resources to illegally hire foreign housekeepers, as a probe into the scandal-hit family widened.
The family of Korean Air chief executive Cho Yang Ho has also been accused of smuggling luxury goods into the country.
Korean Air Chairman Cho Yang-ho on Sunday apologised for the "immature" behaviour of his two daughters and said they would both immediately resign from their company posts following separate controversies.
A Korean Air heiress accused of assault has been suspended by her father's company as police Tuesday launched a criminal investigation into claims she threw water into a man's face in a business meeting.
South Korea's top carrier Korean Air said its staff followed company procedure in restraining an unruly passenger after 1980s pop singer Richard Marx tweeted that he helped the "ill trained" crew handle the situation.
Passengers of a Korean Air plane recalled the terrifying moment one of the aircraft's twin engines caught fire as it was gaining speed for take-off at Tokyo's Haneda airport.