A pathologist found no obvious major injuries to her body, leading to the theory that she was smothered or strangled.
An initial examination apparently uncovered bruising but forensic experts have been hampered by the badly decomposed state of the corpse when it was finally recovered from the sweltering roof space last Friday.
Although Tia had clearly been dead for some time, officers have not been able to rule out that the schoolgirl was alive when colleagues first visited the council house in New Addington, near Croydon, South London, after she vanished a week earlier.