Domestic violence is the leading cause of injury to women between ages 15 and 44 in the United States - more than car accidents, muggings, and rapes combined.
The statement is false.
These were the leading causes of injury to women between the ages of 15 and 44 in the United States in 1996:
This data is taken from the 1996 National Hospital Ambulatory Medical Care Survey Data File, which can be downloaded via ftp from the National Center for Health Statistics. Domestic violence, referred to in the table as "Injury purposefully inflicted by spouse or other intimate", accounts for 2.2% of injuries to women in this age group. Rather than being a larger cause of injury than "car accidents and other things combined", domestic violence causes only one-tenth as many injuries as motor vehicle accidents alone. And as any thoughtful person might expect, as a source of injuries domestic violence is well behind such everyday occurences as accidental falls and cuts.
Domestic violence is a problem. It is not, however, the leading cause of injury to women. It is not even remotely close to it. In the long run we will all be better off if discussion of this subject has some relationship to the real world.