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Officers were called to a McDonald's around 12:40 p.m. Thursday after a stranger gave the baby boy the bottle. The boy drank some of the liquid and threw up.
He was rushed to hospital and police said he is in stable condition.
The bottle and the liquid are being tested, police said.
The Greenwich detachment tweeted a warning that a white woman in her 50s was "giving children in pushchairs bottles containing believed bleach."
Police said there was only one known victim, but warned people to be cautious.