While bullies and their victims traffic in threats, taunts and fights in the schoolyard, a report on Thursday showed those on both sides are also more likely to live with violence at home.

Violent family encounters were most common among youth who identified as someone who has both bullied and been victimized, the report said.

The association was among findings from a study by the Centers for Disease Control and Prevention, which along with the Massachusetts Department of Public Health analyzed data from middle and high school students across the state.

Massachusetts has been at the forefront of the bullying debate since the widely reported suicides of 15-year-old Phoebe Prince of South Hadley last year and 11-year-old Carl Joseph Walker-Hoover of Springfield in 2009.

The state passed anti-bullying legislation in May 2010 which prohibits bullying in school and online, and mandates school-developed bullying prevention and intervention plans.

The CDC analysis, published online in its Morbidity and Mortality Weekly Report for April 22, confirmed some well-documented associations with bullying - an increased likelihood of suicide, substance abuse or poor grades.

But using the Massachusetts data, the CDC also found bullies and their victims reported being physically hurt by a family member or witnessing violence at home significantly more often than people who said they had not been bullied.

CDC’s report established a link between bullying and events outside school.

“A comprehensive approach that encompasses school officials, students and their families is needed to prevent bullying among middle school and high school students,” the CDC researchers said.

The report, which CDC said was the first state-specific analysis of risk factors and bullying, also noted that significant numbers of bullies and bully-victims said they had recently used alcohol or drugs.

SOURCE: MMWR 2011.