This is one of the myths that a lot of former Soviet Union citizens believe themselves. Unfortunately, crime levels isn't a thing that can be accurately reported from your own experience - you have to rely on some objective outside measure. And while any crime-related news (or any bad news, for that matter) were heavily suppressed, soviet police was equally reluctant to open investigations, because of statistic-based reward system in place.

Independent investigations now show that there was actually a lot of everyday crime. Even serial killers were just as common in USSR as they were in US, I've read a whole book about the notorious cases - but while in US media elevated them to celebrity status, in USSR the whole thing was heavily suppressed, and most people only heard rumours.

Please, don't perpetuate soviet propaganda.