KANSAS CITY, Mo. — Breaking their silence for the first time, the family of the woman shot and killed by Chiefs linebacker Jovan Belcher said Monday their ‘‘hearts are truly broken’’ and asked for privacy while they grieve the loss of two loved ones.

Belcher shot and killed his 22-year-old girlfriend, Kasandra Perkins, at their Kansas City home Saturday before driving to Arrowhead Stadium, where Belcher committed suicide in the practice facility’s parking lot, police said. The couple had a 3-month-old daughter, Zoey.