The robbery was reported just after 8:30 p.m. Thursday at the Route 15 Fairfield rest area.
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Officials say the suspect displayed a black handgun while the child stood by the door. The man demanded money from two cash registers -- a register at Dunkin' Donuts and a register from the small convenience store inside the building.
One customer was inside at the time but no shots were fired and no one was injured. The man and child left the area with an undisclosed amount of cash.
Police say the child did not appear to be actively involved in the robbery.
"From a safety standpoint, we want to ID the suspect so we can certainly remove that child from what clearly could be a harmful, hazardous situation and get the child any help he may need," Connecticut State Police Sgt. Thomas Kiely said.
Detectives are also trying to figure out the relationship between the suspect and the child.
The suspect was described as 5 feet 8 inches and was last seen wearing a mask, a black sweatshirt, grey sweatpants and red sneakers.
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The child was last seen wearing a green coat and tan pants.