Police were attempting to pull over the driver on suspicion of drunk driving at the time of the crash.
"The police were chasing him. Then I heard boom boom boom boom," said a witness.
The force of the crash sent one vehicle into the side of a building.
Two people in the vehicle that refused to pull over were rushed to Bellevue Medical Center.
One was in critical condition and the other was serious.
Two people in the other vehicle were treated for less serious injuries.