The body of 25-year-old Lauren M. from Colorado was found on Tuesday night, lying face down on a mattress with splatters of blood on the floor.
Her half-undressed body had been surrounded by a sea of burning candles, according to the APA news agency.
Investigators said the victim was believed to have died from suffocation, but added it was too early to determine whether she had been murdered.
"Further post-mortem examinations need to be carried out," a police spokesman told AFP on Friday.
Toxicology testing has been ordered, although it could be a couple of weeks before the final results are available.
Police have been speaking to the dead woman's neighbours and friends.
Her employers, who described her as "very reliable", had filed a missing person report on Tuesday after she failed to pick up their child from kindergarten.
Firemen then went to the American's one-bedroom flat and broke down the entrance door, leading to the gruesome discovery.
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Lauren M. had been living in Austria for several years and was a German language student.
Local media reported that a Gambian man who had lost his right to stay in Austria had been living with her in the apartment but has since disappeared. However, police have said that so far it is too early to speak of any suspects in the case.