Plymouth has only half the crime that the average American city of similar size has.
Burglaries and thefts are the crimes most often reported. Violent crimes (murder, rape, assault), all total, are less than 70 annually.
There are only 4 sex offenders registered for the greater Plymouth area.
You have about as much chance of running into a criminal as passing a lotto winner on the street.
Use common sense and don't act like a silly tourist and you should be safe in Plymouth.