Police originally received reports that up to ten shots were allegedly fired into a property on Purnell Road in Corio, Geelong, about 2.15am.
Officers were then headed to the scene of the alleged shooting when the driver of a grey Ford sedan allegedly drove onto the wrong side of Purnell Road and tried to ram the police car.
Police then lost track of the Ford and found it a short time later at the intersection of Thompson Road and The Boulevard in Norlane, where the driver rammed an unmarked police car.
Fortunately, no officers were injured in the crash.
The driver of the Ford then fled and dumped the car on Alkira Avenue, where the driver and passenger fled.
Shortly afterwards, police arrested a 23-year-old man and a 43-year-old woman.
They are speaking with police.
Police say they have found no evidence that shots were fired at the address where the shooting was reported.
They have said they do not believe the police car ramming and the alleged shooting are related incidents, after it was early thought they may have been connected.
Anyone who witnessed the incident, has CCTV/dash cam footage or with information about what happened is urged to contact police.