Officials have said the motion would not affect their long search for the military commander during the 1992-95 Bosnian war, as they either had to prove conclusively that he was indeed dead or arrest him if he was alive.
Mladic was charged with genocide by the International Crimes Tribunal for the former Yugoslavia (ICTY) in The Hague, Netherlands in 1995.
He is wanted for allegedly masterminding the 44-month siege of Sarajevo that left 10,000 people dead and the 1995 massacre of around 8,000 Muslim men and boys in Srebrenica.
Tuesday's move has sparked anger from some quarters, with one court official describing it as "mocking the state institutions".
"Thousands of people have gone missing in the wars, but none of their family members asked court to proclaim them dead, although a possibility that they were not alive any more was much higher," Rasim Ljajic, chairman of Serbia's National Council for co-operation with the ICTY, said.
"Mladic's family is announcing this demand exactly because they know he is alive."
Munira Subasic, head of the Women of Srebrenica association, said filing such a request would be a shameful act.
"While we have been fighting for our right to locate the bones of our children for 15 years now, Serbia is finding ways of how to help the family of the most wanted war criminal accomplish their rights," she said.
If Mladic's family are succesful in their bid, it would allow Mladic's wife and son to collect a state pension which has been frozen for more than three years or sell his property, including the family home in Belgrade.
UN court officials believe Mladic is hiding in Serbia, where he enjoys support among nationalist hard-liners who consider him a war hero.
According to Serbian law, people over the age of 70 who have not been heard from for more than five years can be declared legally dead without a heavy burden of proof.
But in the case of Mladic, who would now be 68, the family will have to prove that "he disappeared under such circumstances that make it probable that he is no longer alive".
Vladimir Vukcevic, the Serbian war crimes prosecutor, said in February that the authorities were aware of the general's movements until three years ago, and that Mladic was in Serbia in 2007.
Serbia applied for European Union membership last year, but its progress is linked to Belgrade's full co-operation with the ICTY and the arrest of remaining war crime fugitives.
In recent months, Serbia has stepped up efforts to arrest Mladic, raiding houses belonging to him and his family.