A Mercedes with government license plates struck and killed a police officer on a main street in central Moscow late on September 25.
Footage posted on the Internet shows the Mercedes moving at high speed down a central lane of Novy Arbat Street reserved for cars with special permits and hitting the officer, identified as 32-year-old Senior Lieutenant Sergei Grachyov.
It was unclear who was behind the wheel or riding in the Mercedes.
Russian media reports cited unnamed law enforcement officials as saying the license number indicated the vehicle could belong to the Federal Security Service (FSB), but that was not officially confirmed.
Reports also said police who arrived at the scene removed the license plates and a flashing light from the car and kept journalists at a distance.
There have been several cases in Russia and other former Soviet republics in recent years in which cars used by officials or their relatives have caused deadly accidents.
Russian officials and well-connected people close to the government have been accused of abusing special road privileges by using blue flashing lights and sirens.
In 2011, members of a protest movement called the Blue Buckets drove around Moscow with blue toy buckets on top of their cars, mocking the elite's flashing blue lights.