The number of people who fear drug dealing or mugging is taking place in their community has risen slightly for the first time in five years.
But the official figures also said almost three quarters of adults believed overall crime rates where they live had remained the same or reduced.
The findings are in the Scottish Crime and Justice Survey of 16,000 people.
A further finding was that 58% of people believed local police presence was not sufficient in their area.
The survey also revealed that 31% of people felt officers were not dealing with the things which mattered to them.
The Scottish government welcomed the survey, saying it showed the majority of people believed crime rates in their local area had remained the same or fallen in the past two years.
Justice Secretary Kenny MacAskill said: "These are welcome trends which show that we are making progress in our fight against crime in Scotland's communities.
"Recorded crime in Scotland is at its lowest level in 32 years, there is an all-time record number of police officers - over 1,000 extra since March 2007 - on Scotland's streets making our communities safer, and now today's survey shows Scots are also feeling safer in their communities.
"What we are seeing here is a downward trajectory right across the board - crime is down, your risk of being a victim is down, communities are becoming safer and Scots are feeling more positive in 2010 as a result. That is to be welcomed."
However, he added that it was important not to be complacent and efforts would need to be made to drive down crime even further.
Scottish Labour's justice spokesman Richard Baker said that recorded crime figures were "meaningless" because fewer and fewer people were reporting crime in the first place.
He added: "Violent crime is still running at a much greater rate than the rest of the UK and the dangerous and underfunded plans to scrap short sentences and replace them with community service are not supported by the vast majority of Scots.
"With the SNP's 'here today gone tomorrow' police pledge it's likely that even fewer people bother reporting crime in the future. The survey made clear that two thirds of people believed local police presence was not sufficient in their area."
Scottish Conservative community safety spokesman Bill Aitken said: "The SNP government's determination to empty our jails and put more criminals on community sentences is clearly hugely unpopular with Scots all across the country.
"A drop in crime is encouraging, even if only 37% of crimes are reported at all, but what we must not forget is that Scottish Conservative pressure for 1,000 more police is hugely influential here."
Scottish Liberal Democrat justice spokesman Robert Brown said drink was a major factor in offences.
He added: "Liberal Democrats want to see a major crack down on the selling of alcohol to people who are under age or already drunk.
"Eighteen per cent of all violent crime is committed around pubs and nightclubs. Urgent action must be taken to target these nightspots, especially at the weekend."
Some of the key findings in the survey included;
- 19.3% of adults are victim of at least one crime with 88% of them victim of property crime
- crime appears to have fallen by 10%, and the risk of being a victim fell from 20.4% to19.3%
- 52% of those surveyed believed crime rates had increased in Scotland as a whole
- 68% of those asked were confident in the police's ability to investigate incidents
- 56% felt the police's presence in their local area was insufficient with 65% in most deprived areas
- 85% agreed that community sentencing was a good idea for minor crimes
- 66% felt drug users needed treatment not prison
- and 64% believed community sentences were a soft option, and did not punish enough