It comes after a nearby school was sent into lockdown.
Officers were called to reports of a firearms discharge shortly before 3.30pm in Grebe Drive on Wednesday (04/11).
As a precaution, a lower school in close to the incident went temporarily into lockdown, with specialist armed officers deployed to the area.
The officers quickly identified a vehicle believed to be at the scene of the incident, with a pursuit then taking place along the A505 before the car stopped in Porz Avenue, Dunstable after colliding with an unrelated vehicle, the driver of which was treated for minor injuries at the scene.
Police say the three occupants of the suspect vehicle then fled the scene on foot, with two running in the direction of woodland near Nimbus Park. One was described as a black male with dreadlocks, wearing black clothing with white socks and black sliders. The third man ran in the direction of Lovett Way.
Detective Inspector Stephanie Garfitt from Bedfordshire Police's Crime Investigation Department, said: "This was a shocking incident; the safety of the public is always our highest priority and we are following several lines of enquiry to find those involved.
"This incident happened in close proximity to a lower school, and as a precaution, the school carried out its safety procedures as a matter of course.
"This understandably adds to the concerns within the local community and we will maintain a high visibility presence while our investigation continues.
"We are appealing for anyone who may have witnessed the incident, or has doorbell or dashcam footage from the area, of either the activity in Leighton Buzzard or Dunstable to get in touch.
Anyone with information about those involved, is also asked to contact us, either online or via 101 quoting Operation Tanglewood."
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