The incident took place yesterday when the girl's parents, who are migrant labourers, had gone out to work while their two other children were at school.
"The three-year-old girl was alone at home. When her parents returned they found her lying unconscious in a pool of blood," the officer said.
He said the girl had severe injuries on her private parts.
"The girl was rushed to a hospital for treatment where the doctors confirmed rape. The condition of the girl continues to be critical," the officer said.
"A case against the unidentified person has been registered and investigations have started to nab the culprit," he said.