Theft or violent crime struck one out of every four American homes in 1987, about the same rate recorded in the previous two years, the Justice Department reported Sunday.

The Bureau of Justice Statistics said 23.9 percent of white homes, 27.8 percent of black homes and 30.1 percent of Hispanic homes were hit last year by some sort of crime. The national average was 24 percent.Homes in the Northeast were the least affected, 19 percent, while those in the West were the most vulnerable, at 29 percent. The rates were 25 percent in the Midwest and 24 percent in the South.

Since the bureau began collecting crime data on a household basis in 1975, when crime struck one in three homes, the rates have never shown a year-to-year increase and dropped substantially over the longer term.

Bureau Director Steven R. Schlesinger noted that there was greater improvement among white households than among black ones. From 1975 to 1987, the rate dropped 25 percent for white homes, whereas the decline for black homes was 15 percent. The difference was due primarily to the fact that thefts from black homes failed to decline, while the reduction in other types of crimes was about the same for both white homes and black homes.

The household rates are derived from the National Crime Survey, which has interviewed about 99,000 people of age 12 or older from a sample of 49,000 homes around the nation.