As the number of homicides in New York has reached historically low levels, the Police Department has intensified its efforts to combat a particularly stubborn and daunting source of murders: domestic violence.

Over the past several years, the department has bolstered the size of the staff at its domestic violence unit by about 40 percent, with 450 police officers now focused on families with histories of violence. The police are now making more domestic violence arrests, while murders linked to domestic violence appear to have declined slightly.

As part of their work, the officers assigned to the domestic violence unit make a total of 70,000 precautionary visits a year to the households with past episodes. Each precinct station house also maintains a “high propensity” list of a dozen or so households that get special attention because they are believed to be most at risk of further violence.

In their visits, the police devise safety plans with the victims and check for evidence of further abuse and, when a past abuser is barred from the home, signs of his return. “You look to see if she has any bruises; you’re looking around the house to see if the furniture is broken,” said Detective Dale Edwards, describing what she does during a home visit. “You inquire. You try to be tactical about it.”