Maidstone and Tunbridge Wells NHS Trust is the first trust in the country to face such a charge since the offence was introduced in 2008.
It follows the death of primary school teacher Frances Cappuccini, 30, after an emergency caesarean section in 2012.
Anaesthetist Errol Cornish, 67, is separately charged with gross negligence manslaughter. Prosecutors are also seeing the extradition of anaesthetist Nadeem Azeez, 52, who faces the same charge and is believed to be in Pakistan.
Sitting at Maidstone crown court, Judge Philip Statman said: “This is a unique prosecution. it is the first time an NHS trust has been prosecuted for corporate manslaughter.” He said that given this was the first prosecution of its kind, it was right that a high court judge should try the case.