“I knew I needed an interpreter and had a right to an interpreter,” she said. “I was denied the right to speak. I was denied to the right to express myself. I felt destroyed,” she said in Spanish during an interview.

Ms. Macareno, 30, an undocumented immigrant from Mexico, is hardly alone among women in New York who say they have tried to report abuse to the police only to be foiled by a persistent language barrier that critics say has devastating consequences for victims of domestic violence.

In a city where more than half the 8.5 million residents speak a language other than English at home, and one in four struggles to communicate in English, it is common for a crime victim to be met by police officers who do not understand the victim’s language.

Ms. Macareno was one of several women who filed a federal discrimination lawsuit against the city in 2013, claiming that the police violated their civil rights by denying them interpreters. The parties reached a settlement this month that requires the police department to adopt new protocols and training for officers responding to domestic violence incidents involving victims and witnesses who do not speak English well.

Under the terms of the agreement, which was approved on Wednesday by a federal judge in Manhattan, the police department will train officers over the next 18 months on when to call on an interpreter and how to use their department-issued smartphones to reach a city-contracted service that provides immediate access to interpreters in more than 240 languages.