The ambulance service were called at around 12.05am following reports of concerns for a woman in Victoria Road, and subsequently alerted the police.
Officers have now launched an investigation to establish what caused the woman to become unresponsive. She was taken to hospital where she remains in a critical condition.
Detective Inspector Jackie Dadd said: “A woman is critically ill in hospital and it’s important that we investigate what has caused this. I would appeal for anyone who noticed anything unusual in Victoria Road prior to 12.05am or anyone with any information to get in touch.”
Anyone with information is asked to contact police on 101 or call Crimestoppers, anonymously, on 0800 555 111.