Emma Faulds went missing from her Kilmarnock home more than a week ago and has not been seen or heard from since.
Her family, who reported her missing to police last Tuesday, are “extremely upset”.
Officers have said they now fear the 39-year-old “may have come to harm”.
Ms Faulds was last seen at around 9.10pm on the evening of Sunday 28 April in the Monkton area, about 12 miles from Kilmarnock.
A forensics team has been searching a detached house in Fairfield Park in Monkton as part of the inquiry.
A major public appeal for information has been launched, with family members insisting the disappearance is “totally out of character”.
Ms Faulds is described as white, around 5ft 3in tall, with a slim, athletic build, long blonde hair, a pale complexion and blue eyes.
She usually drives a light blue BMW 1 Series M Sport with the distinctive number plate F5 EMA.
The car, which was found outside her home, has been removed by investigators and is undergoing a full forensic examination.
Specialist officers have been searching areas and properties around Monkton, including two other cars which are also being inspected.
Police continue to review CCTV footage for any sightings of Mr Faulds or her car.
They want to hear from anyone who may have seen the car being driven in the Monkton or Kilmarnock areas on the night of Sunday, April 28, or the following morning.
“Emma is in constant contact with her family and friends and the fact that she has not been heard from is alarming,” said Detective Chief Inspector Martin Fergus, from Police Scotland’s Major Investigations Team.
“Emma also has a dog, a west highland terrier, and she would never leave it for any length of time without ensuring someone is able to look after it.
“We are liaising with Emma’s family and we now believe that she may have come to harm.
“Emma’s car has been removed for examination and I am appealing to motorists, taxi drivers or members of the public who may have seen it being driven in the Monkton and Kilmarnock areas late Sunday night into Monday morning. I would ask people with dash cams to check their footage as they may have captured the car and not realise its significance.
“You may have noticed the registration number but thought nothing of it at the time, but now where and when you saw it could be vital.”
He added: “Emma is a sociable outgoing person who enjoys seeing her family and friends. They are distraught at not knowing where she is or what may have happened to her.
“I would appeal to anyone who may have information or knowledge as to her whereabouts to contact us.”
He called on anyone who had seen her in the days before she went missing to come forward in case they have information that could prove significant.