Deputy Foreign Minister Rakhat Aliev, who is married to Darigha Nazarbaeva, is suing a retired intelligence service colonel, Arat Narmanbetov, for slander. Narmanbetov has accused Aliev of being behind the slaying of Altynbek Sarsenbaev, a leader of the opposition party Naghyz Ak Zhol (True Bright Path).
Sarsenbaev and two aides were killed on February 11. Police say they believe the murder was motivated by personal enmity.
The opposition says Sarsenbaev's murder was politically motivated and is demanding that Aliev and his wife be interrogated.
Narmanbetov pleaded not guilty.
The court adjourned until April 24 after calling as a witness Nartai Dutbaev, a former head of the Kazakh intelligence service (KNB). Dutbaev resigned after five of his employees were arrested for their alleged involvement in Sarsenbaev's slaying.