Emergency services were called to the scene at Roborough Close in Bransholme just before 4am on April 18.
Several homes were gutted in the fire.
Initial enquiries suggest the blaze was started through criminal activity and a joint police and fire investigation is currently underway.
A spokesman for Humberside Police said the flat had previously had its water, gas and electricity cut off and had remnants of copper on the floor, and no accelerants were found.
He added that the two most likely reasons for the fire were that it was either used for stripping wire and copper or that the incident was arson.
He said: “As a result of the fire taking hold, the flames and in particular the toxic smoke has then travelled into the roof space of all the terraced flats.
“As all the homes were occupied by sleeping families, this could have been fatal, had the fire brigade not arrived in the short time they did.
“A two-year-old little girl was taken to hospital as a precautionary measure and later discharged.
“Six flats where affected, with the next door neighbour’s roof fully collapsing inwards, another suffering extensive water damage, and all displaying smoke damage.
“Fortunately no one was killed or injured, but this has posed the question, how valuable are the lives of the people living around the flat, which was suspected of being used for burning copper?”