The cars collided in a residential road in Cradley and one of the vehicles crashed into a lamppost at around 11.25pm on Friday.
Both cars were abandoned as the people inside fled the scene in Clent View Road.
The 999 caller reported hearing a gunshot but police are yet to find evidence to support the account.
A spokesman for West Midlands Police said: "Police received a call at 11.25pm last night reporting a two-vehicle collision in Clent View Road, Cradley, in which one vehicle hit a lamppost.
"It’s understood the occupants of both vehicles fled the scene; the vehicles have been recovered by police.
"The initial 999 caller also reported hearing what they believed to be a gunshot.
"Police have searched the scene and there is no damage consistent with a firearms discharge and no evidence at the scene to corroborate the account at this stage."
Clent View Road is made up of semi-detached houses and connects High Park Road and Meres Road near Caslon Primary Community School and Cradley Town FC.