The force voluntarily referred itself to the Independent Police Complaints Commission (IPCC) after the blaze in Dinnington on November 1.
A 35-year-old woman was taken to Rotherham District General Hospital after being rescued by firefighters and was later released.
The IPCC says it assessed the material referred to it by the force and has launched an independent investigation “that will examine South Yorkshire Police’s response to a number of calls made to the force”.
Police arrested Liam Fretwell, 23, and Carly Waddington, 19, shortly after the fire. They were charged with arson with intent to endanger life and appeared at Rotherham Magistrates’ Court on 4 November.
The pair had their first appearance at Sheffield Crown Court on Monday and are due to appear again at the same court on January 22. They are both also charged with possession of a Class B substance.
IPCC Commissioner for Yorkshire, Cindy Butts, said: “Our investigation will examine the contact between the woman and South Yorkshire Police to ascertain whether the correct procedures and policies were followed, and also whether anything further could have been done prior to the fire at her home on 1 November.”
A South Yorkshire Police spokeswoman said: “South Yorkshire Police can confirm it has voluntarily referred itself to the Independent Police Complaints Commission following a house fire in Dinnington on 1 November. The force will co-operate with the investigation.”
Police said at the time that officers “used fire extinguishers from their vehicle to put out the flames” from the fire on Manor Road, which started around 5am.
The force said: “A 35-year-old woman from the house was taken to Rotherham District General Hospital where she was treated for smoke inhalation and burns to her face. Nobody else was injured.”