The Serbian Justice Ministry said in late February it had issued an extradition request for Milosevic's widow, Mirjana, and their son Marko, currently living in Moscow. Russia granted the Milosevic family refugee status in February 2006.
Mirjana and Marko Milosevic are wanted in Serbia for heading a cigarette smuggling ring in the early 1990s, which investigators say netted them several million dollars. The mother and son have denied the allegations and have refused to return to their homeland to face trial.
Marko Milosevic has also been charged with causing grievous bodily harm to members of an opposition movement during a skirmish in 2000.
About 20 witnesses have been questioned in the case, two of whom testified during the court hearing in the Serbian town of Pozarevac.
The next hearing is due on April 9.
A spokesman for the Russian Federal Migration Service said last month that the service saw no grounds for the extradition of Mirjana and Marko.
Slobodan Milosevic, who led Yugoslavia into war and international isolation, culminating in the NATO bombing of the country in 1999, died in custody at The Hague in March 2006, before a UN war crimes tribunal passed a verdict on his role in the wars in Croatia, Bosnia and Kosovo in the 1990s.
The former leader died of a heart attack, although he had previously complained of chest pains and requested permission to undergo treatment in Moscow, which was denied.
Milosevic's brother Borislav, a former Yugoslav ambassador to Russia, also lives in Moscow.