The incident happened at around 4.10pm on Friday when a Volkswagen Polo and a Vauxhall Mokka collided on Academy Street at its junction with West Abbey Street.
An 88-year-old man and a 76-year-old woman were treated at the scene for minor injuries but did not require hospital treatment.
Police Constable Derek Miller said: “It is vital that we establish exactly what happened here. Although we have already spoken to a number of people who were in the area at the time, we would ask those who have not spoken to us to come forward.
"Also, if you have any dash-cam or security footage from the time of the incident I would ask you to get in touch.”
Anyone with any information should contact Police via 101 quoting incident number 2351 of Friday, November 19, 2021.