Port Elizabeth police are desperately trying to find the family of a 2-year-old boy who died at a local hospital after being brought in by an unknown man who later "fled".

Police said they had opened an inquest docket after the child died at Livingstone Hospital shortly after being dropped off on Tuesday.

"According to personnel at the hospital, an unknown male brought the child in at about 3.40pm, informing them that [the child] had fallen off the bed and needed treatment. While doctors were treating him, he died," said police spokesperson Sandra Janse van Rensburg.

Janse van Rensburg said Gelvandale detectives were urgently trying to trace the parents of the boy after the man who bought him to the hospital allegedly fled.

"When they approached the unknown male to inform him of the death, he ran away. No information of the child or the coloured male is known," said said.

The inquest docket is pending the results of a post mortem.

Police are appealing to anyone who may know the parents or the child to urgently contact Detective Warrant Officer Neil Hendriks at SAPS Gelvandale on 082 442 1816 or Crime Stop on 0800 10111, or their nearest police station.