Armed police were called to a street in Batley following reports of gunshots, hours after a car chase through the streets of the town.
They visited Conway Crescent at around 1.30am on Saturday September 13, but found the street to be empty.
Police are linking it to a car chase which happened at around 6pm on Friday September 12.
A red Audi was being pursued by a Volvo along Upper Road, which continued into Halifax Road before going into the car park at Staincliffe Hospital.
One of the passengers in the Volvo was seen leaning out of the window, possibly holding a gun. No shots were fired.
Police are now appealing for further information.
Detective Chief Inspector Steve Snow, of Protective Services (Crime), said: “Due to the manner in which these two cars were seen driving and the fact they entered a hospital car park, we believe that someone will have witnessed the incident or perhaps made a note of their registration plates, as they nearly caused a collision with other vehicles as they entered Halifax Road from Upper Road.
“We would like to speak to anyone who witnessed cars of these descriptions driving erratically in the area at just before 6pm yesterday, or anyone who saw a silver/grey Volvo V60 being abandoned in suspicious circumstances at any time after 6pm.
“We would also like to hear from anyone who saw a black car leaving Conway Crescent around the time that the shots were heard.
“High visibility patrols will continue in the area today and will speak to residents about any concerns they may have.”
Contact police on 101 or Crimestoppers on 0800 555111.