The authorities reopened an investigation of Liechtenstein-based Bambino after Ecclestone appeared in court in Germany last year on bribery charges.
That case in Munich was settled by Ecclestone paying a $100 million fee.
It arose after claims that a controlling stake in Formula One held by German bank BayernLB had been undervalued when sold to private equity fund CVC as a result of a "corrupt bargain" between Ecclestone and former BayernLB banker Gerhard Gribkowsky.
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Gribkowsky was jailed by a Munich court in 2012 for tax evasion and corruption for taking a $44 million payment from Ecclestone and his family trust.
Ecclestone argued that the payment was unrelated to the sale and was made because Gribkowsky was threatening to make false claims about the Briton's tax affairs.
The Formula One supremo has said management of the trust funds, set up for the benefit of his ex-wife Slavica and daughters Tamara and Petra, is nothing to do with him and he is not a beneficiary.
Ecclestone said on Thursday that remained the case.