Beginning in 1972, the Gallup Poll asked "is there more crime in this area than there was a year ago, or less?" Around 1990, they switched to asking about "your area," but it doesn't seem to have made much difference (a Los Angeles Times poll asked the old form in 1994, so there's a little overlap). I calculated a summary of perceptions: the logarithm of the ratio of "more" to "less" answers. It would have been simpler to use percent saying more to percent saying less, but there seems to have been a long-term decline in the percent volunteering "about the same," and using the logarithm of the ratio takes that out of the picture.
Positive numbers mean that the number who thought there was more crime was larger than the number who thought there was less. It was positive in most years, but for a few years around the turn of the century the number seeing less crime was larger than the number seeing more. The numbers seeing an increase in crime are generally smaller today than they were in the 1970s. The crime rate has indeed fallen, so that raises the question of whether perceptions are related to reality. I regressed the ratio on the change in the national homicide rate in the last three years. Homicide is only one form of crime, but it's measured more accurately than other forms, and gets more media attention, so it seemed like the best place to start. I used the last three years rather than the last year because I figured people probably didn't take the time frame all that literally, but just treated it as meaning "recently."
There is a positive relationship between change in the murder rate and perceptions of change in crime, with a t-ratio of 2.7 and 3.2 depending on the exact model. There is a good deal of inertia*, so it takes a while for changes in reality to show up in people's perceptions, but they do show up.
*The coefficient on the previous value of perceived change in crime was about .9**t, where t is the gap of time in years. That means that a change in the murder rate would have a "half-life" of about 7 years in terms of its effect on perceptions.
[Data from the Roper Center for Public Opinion Research]