A number of calls were received shortly after midnight when people reported seeing the woman with a man in a car in Woodhall Road, Calverley.
The car, which was near the junction with Oastler Road, drew attention because its horn was beeping at around 12.05am today.
It then drove off at speed along Woodhall Road towards Thornbury, with the woman still inside.
Detectives are continuing enquiries to identify the people and the vehicle, which was described as possibly being a silver Vauxhall Astra or Corsa.
Detective Inspector James Entwistle, of Leeds District CID, said: "The people who contacted us were understandably concerned about the welfare of the woman involved and we are carrying out enquiries to trace the vehicle and establish the circumstances surrounding the incident.
"We have not had any missing person reports or other concern calls that match to this incident.
"It may be that there is an explanation for what people saw and we would ask that the people involved or anyone with any information that could assist the investigation contact us immediately."
Anyone with information is asked to contact Leeds District CID via 101, quoting log number 10 of July 11.
Information can also be passed on to independent charity Crimestoppers anonymously on 0800 555 111.