Authorities released few details about the deaths, saying they were still notifying relatives. But Arlington Police Chief Frederick Ryan said police were not looking for any suspects and there was no reason for the public to be alarmed.
"We're quite certain that the community is safe and people can go out and go about their business this evening," he said.
An officer found the bodies in the two-family home in a quiet residential neighborhood around noon. Authorities did not say how long they had been there.
"This is obviously a very troubling, very tragic situation," said Middlesex County prosecutor Marian Ryan.
Ryan would not say how the four died.
Stephen Trebino, who grew up across the street, said a husband and wife lived in the house and he often saw one of them walking with the babies. He said the man was nice to his father and would shovel the walk without asking when it snowed.
"He was friendly," Trebino said. "He was always working on the house, always go, go, go."