The two appeared on charges relating to a stolen car found on their property.
They were arrested on February 28 and were both released on a warning the same day, after Krejcirova lodged an urgent application in the High Court in Pretoria.
She was arrested at the Palm Ridge Magistrate’s Court while attending her husband’s bail application.
On Thursday, the prosecution requested the postponement as investigations were still ongoing.
Krejcirova and Dennis’s lawyer Annelene van der Heever opposed the “lengthy postponement” sought by the State.
“We offered the SA Police Service an opportunity to consult with the accused. They [police] went ahead and arrested them. Now they tell this court that they are still investigating.”
She said police had arrested the two without investigating the matter.
A trial date would be set when the case returned to court on April 10.
The State alleges that the two bought a Volkswagen Amarok using falsified documents.