A woman in her 60s was killed in the incident involving a black Renault Clio she was a passenger in.
The crash happened between the resort and Penrhyn Bay, on a bend on a lane near Glanwydden, some time between 17:30 GMT and 21:30 on Friday.
The driver was also injured when the vehicle left the road and careered into a field.
She was taken to hospital in Stoke with serious, but non-life threatening injuries.
Police want to speak to the driver of a van who may have information about what happened.
North Wales Police Sgt Nikki Grimes-Williams said; "We understand that at about 6.15pm last night, a small van or SUV type vehicle was seen parked on the grass verge in Gloddaeth Lane close to the scene of the incident.
"I am appealing for the driver of this vehicle or any passengers to come forward."
An inquiry has been launched following a fatal car crash near the Conwy seaside town of Llandudno.