The vehicle drove off, pursued by dozens of police cars, and is now involved in a stand-off in a car park, officials said.
Police said officers responded to a call for an active shooter at the police headquarters at 12:27 AM. Shots were fired at the building, police said.
There has been an exchange of gunfire in the car park, police added.
A bag left outside the police station was later confirmed to contain explosives including pipe bombs, police said on Twitter.
A possible suspect has been identified as James Boulware, police said.
The motive for the shooting is not yet clear.
Dallas police say no police officers have been injured.
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