They say Aisling McCarthy Brady, who lives in Quincy, arrived from Ireland in 2002 on a tourist visa and could stay up to 90 days.
The 34-year-old is being held on $500,000 bail after her arraignment Tuesday in Cambridge District Court.
She pleaded not guilty to a charge of assault and battery on a child causing injury.
The child was hospitalized Jan. 14 with what authorities described as head injuries and healing bone fractures, but was declared brain dead two days later.
Authorities say the nanny was the only one with her when the injuries occurred.
Brady’s defense attorney says the injuries could have happened at any time.