Police are trying to piece together reports of a distressed woman with a man in a car beeping its horn just after midnight in Calverley.
Detectives are appealing for information about the suspicious incident in Woodhall Road, near to the junction with Oastler Road.
The car, which was described as being possibly a silver Vauxhall Astra or Corsa, then drove off at speed towards Thornbury.
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 should contact Leeds District CID via 101 quoting log number 10 of July 11 or call the independent charity Crimestoppers anonymously on 0800 555 111.
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules here