In April 1965, the Gallup Poll asked "In some places in the nation, there have been charges of police brutality. Do you think there is any police brutality in your area, or not?" The question has been repeated a number of times--the most recent that has reached the Roper Center was in 2005, although hopefully they have asked it within the last couple of months. The percent saying "yes":
A similar question was asked in 1970 and 1991: "When you hear charges of police brutality, how likely do you think it is that the charges are justified----very likely, fairly likely, not too likely, or not at all likely?" In 1970, 9% said very likely and 27% fairly likely; in 1991, 22% said very likely and 46% fairly likely.
PS: The question was also asked of a sample of blacks in May 1969: 40% said yes, 38% said no, and 23% weren't sure.
[Source: iPOLL, Roper Center for Public Opinion Research]