North Street was closed this morning from the A64(M) New York Road junction to the Byron Road junction to allow investigations at the scene. It has since reopened.
Police believe shots were fired at an Audi on Burmantofts Street from a Ford Mondeo shortly before 6pm.
More shots were fired at the Audi by the same car on North Street a short time later.
The 28-year-old Audi driver was uninjured.
Specialist teams have been conducting extensive forensic enquiries at both locations.
Detective Chief Inspector Nicola Bryar of the Homicide and Major Enquiry Team said: “This is clearly a very serious incident where shots have been discharged in busy streets on a Saturday evening when a number of members of the public were in the area.
“From initial accounts, we believe a number of shots have been fired from a light coloured Ford Mondeo towards a dark coloured Audi at Burmantofts Street and again at North Street before the Mondeo made off at significant pace away from the scene.
“We are conducting extensive enquiries to identify those responsible and to establish the circumstances surrounding this incident.
“We would like to hear from anyone who was in the area around either location yesterday evening and who may have seen either of the vehicles described, who may have witnessed either incident or anyone who has any information that could assist the investigation.
“Clearly an incident of this nature will cause understandable concern and local officers will be conducting additional patrols of the area to reassure the community.”