Francisco Hernandez, 35, of Hartford was said to have fled police when they tried to pull over his car.
Police said that Hernandez was critically injured when he was shot by officers and crashed into a tree.
State police said they tried to stop the driver in Ledyard just before 11:30 p.m. after he almost struck a cruiser.
Troopers and local police gave chase and deployed stop sticks to try and stop the driver. They said the vehicle then pulled into a residential driveway, turned around and sped at an officer who had left his cruiser.
Police say two Ledyard officers fired shots at the driver, who was struck and then drove into a tree.
Hernandez was taken to Yale-New Haven Hospital in critical condition.
The investigation into the incident is ongoing.