When a dog mauled a Bronx toddler, Makailah Barnett, in 2004, it was unclear at first which of the family’s three canines — the bulldog, the pit bull, or the mutt — was the culprit.

A jury in the Bronx just last week fixed the blame not only on the pit bull, but also on New York City, paving the way for Makailah’s family to receive millions of dollars in damages.

Makailah’s mother, Shannon Smith, received the dog from a police officer the day before the mauling, according to the complaint filed in the suit.

The unusual circumstances behind Officer Sean Smith’s decision to give the dog to Ms. Smith, a stranger, were enough to make the city liable for the attack, the jury decided. The day before the mauling, the pit bull was being kept at the 43rd Precinct after police found it abandoned near the station. Ms. Smith was at the precinct at the same time, waiting to file papers in an adoption proceeding. Officer Smith struck up a conversation with her about the dog and Ms. Smith ended up taking the animal home.

A lawyer for Ms. Smith, Thomas Minotti, said Officer Smith was looking to give the dog away and had told Ms. Smith that it would soon be put to sleep.

A spokeswoman for the city law department, Laura Postiglione, said Ms. Smith had “asked to take the dog home.”

It also appears the transfer may have violated a law requiring authorities to hold found animals for five days to give owners a chance to recover their pet or livestock.

“The officer was supposed to take it down to animal control, but he didn’t do that,” a lawyer for Ms. Smith, Thomas Minotti, said. “He wasn’t allowed to give the dog away.”

The jury has not yet fixed damages, but Ms. Smith’s legal complaint asks for $10 million. Makailah was nearly killed in the attack and has undergone five plastic surgeries, Mr. Minotti said.