The crash happened around 7.25pm on Sunday, 17 May, on South Street, between the roundabout junction with the A955 and Dubbieside and involved a silver Volkswagen Bora which collided with a tree.
A 27-year-old female passenger suffered serious injury and was taken to Ninewells Hospital where she remains in a critical condition. The other passenger, a 3-year-old girl, also sustained minor injury and was taken to Victoria Hospital for observation.
The 33-year-old male driver suffered minor injury and did not require any medical attention.
The road was closed for approximately seven hours for collision investigation to be conducted at the scene and to allow for uplift of the vehicle.
Sergeant Ewan Pearce of the Road Policing unit said: “This was a serious crash and our thoughts are with the family and friends of the woman who has suffered serious injury as a result, along with all those involved.
“Our enquiries into the cause of the crash are continuing and I would ask anyone who saw what happened, and has not yet spoken to officers, to come forward.