The operation, which involved two firearms warrants, was carried out yesterday (Monday) in Manningham.
Police searched properties in Oak Lane and Devonshire Terrace but made no arrests and did not locate a weapon following the incident, which reportedly happened in Thorn Lane at 5.20pm on Sunday.
However, while officers were searching the properties, police received a report of gunshots being fired in Marlborough Road nearby at around 6.30pm yesterday.
Officers found a white Porsche Panamera car in Carlisle Road with damage to the front passenger door.
A West Yorkshire Police spokesman said: "The vehicle was recovered for further forensic examination.
"These incidents are believed to be linked and enquiries are continuing to locate the suspects involved.
"Anyone who can assist these enquiries is asked to contact Bradford District CID on 101, quoting log 1475 of 29 May."
Information can also be given anonymously via the independent charity Crimestoppers on 0800 555111.