First Selectman Norman Needleman said there were multiple locations involved and that the situation appears to have ended at the Griswold Inn.
Troopers said the two people were injured during some kind of fight at the Bestway Sunoco gas station on Saybrook Road.
Needleman said a man and a woman were stabbed. They were taken to local hospitals for treatment, and troopers said serious injuries were reported.
The Connecticut State Police Central District Major Crime Squad has been called in to investigate.
State police said they are searching for a suspect and a vehicle in connection to the incident.
In a photo released by police, the suspect appears to be wearing a blue sweatshirt, khaki shorts and white sneakers.
The vehicle troopers are searching for is described as a possibly dark-colored, newer model Alfa Romeo Stelvio.
An NBC Connecticut crew reports at least three scenes in town - the one at the Sunoco, one at the Griswold Inn on Main Street, and a third off of Ferry Street. A witness described seeing a vehicle with damage slowly driving the wrong way on Main Street.
"I guess some really awesome EMT volunteers pulled the guy out of the car and the woman that was with him was very distraught. And the guy pulled out of the car he got put right there and he was bleeding from his face and his abdomen and he was yelling and was super disoriented and they got him out of the car," Marissa Nardone, of Killingworth, said.
Police have not provided more details at this time. Needleman stressed that while the investigation is ongoing, everything is safe.
Anyone with information is asked to contact Detective Derek McGregor at Derek.McGregor@ct.gov or (860) 883-0928.