Supermodel Bar Refaeli is under investigation in her native Israel over allegations that she evaded paying local tax on earnings from her international career.

Lawyers for the 30-year-old, who Israeli media have reported is worth up to $20 million, rejected the accusations.

Her lawyers said the case centred on a long-running dispute with Israeli authorities over whether Refaeli, a former Sports Illustrated swimsuit cover model, should be considered a resident of Israel for tax purposes.

The authorities’ investigation of Refaeli was the worst-kept secret in Israel this week, although a gag order kept her name and face out of the media.

That was lifted on Thursday, in tandem with a court hearing at which she was not required to appear.

Yair Rabinovich, a former Israeli national tax commissioner, said on Israel Radio that her residency classification depended on a combination of factors, including the number of days spent in the country and whether Israel was at “the centre of one’s life”.

Court papers filed by tax investigators and released to the Israeli media said Refaeli had lived in luxury apartments in Tel Aviv in recent years but that her brother and mother had signed the leases to conceal her residency and evade potential tax bills on millions of dollars in foreign earnings.

Media reports said the authorities were also looking into whether tax should have been paid on “celebrity discounts” and perks such as cars that the model had received in Israel.

Refaeli, a former host of the music talent show X-Factor Israel, was questioned for 12 hours by tax investigators on Wednesday. She was not taken into custody, but a Tel Aviv court ordered that she request approval from tax authorities and post a $65,000 bond before any future overseas travel.

Refaeli, who for a time dated Hollywood actor Leonardo DiCaprio, married an Israeli businessman in September at a wedding attended by more than 300 people.