Nearly 25 million American households -- three in every 10 -- were affected by crimes involving theft or violence last year, according to a Justice Department study released yesterday.

The study found that crimes such as rape, robbery, assault by strangers and household burglaries affected one household out of every 10, with some households being victimized more than once. Homicides were not included in the study.

"U.S. families are more prone to have a member attacked in a serious violent crime . . . than to have a residential fire or have a [family] member injured in an automobile accident," it said.

The most common type of crime affecting families was larceny -- pockets picked, purses snatched, and thefts with no forced entry, such as sports or lawn equipment stolen from a back yard. More than 21 percent of all families in the country were victims of that type of crime in 1981.

Nearly 35 percent of black families were touched by crime, compared to about 29 percent of white families. City dwellers are more likely than residents of the suburbs to be victimized by crime, and families in rural areas are even less likely to be crime victims.

Families at all income levels seem to be affected about equally by crime, according to the study. The one exception is families with income over $25,000, who are about twice as likely as families earning $7,500 or less a year to experience simple larceny. Lower-income families are more likely to be victimized by burglary.

Of the 10 percent of all households victimized by more serious crimes, the study found that 7 percent experienced at least one burg-lary in 1981 and 6 percent had at least one victim of violent crime, either by a stranger or an acquaintance. The numbers total more than 10 percent because some households were victims of burglary and a violent crime such as assault, rape or robbery.

The study found that the crime rate of 30 percent of all households remained steady from 1980 to 1981 and that it has decreased slightly since 1975 when 32 percent of all households were affected by crimes involving theft or violence.

Another federal study, published simultaneously, indicated that serious violent crime did not increase between 1973 and 1980. In that period, serious assaults fell by 8.5 percent, household burglaries by 8.2 percent and motor vehicle theft by 12.3 percent. During the same period, simple assaults, which did not involve serious injury, rose 11 percent.