Here ya go.
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Rural America Reels From Violent Crime. ‘People Lost Their Ever-Lovin’ Minds.’
Murder rates didn’t soar only in cities during the pandemic. Homicide rates in rural America rose 25% in 2020, the largest rural increase since the CDC began tracking such data in 1999. Small-town sheriffs and prosecutors are overwhelmed with homicide cases.www.wsj.com
That's only talking about increases in violent crime, not absolute levels over the long-term.
I'm sure there _are_ rural areas that have high crime rates - I recall reading that Albania (not a heavily urbanised country) has a problem with multi-generational murderous feuds between families. So I guess it's quite possible to have a long-settled population where everyone knows everyone else, but who nevertheless murder each other on a fairly regular basis!

Albanian Blood Feuds: More Than 10,000 Revenge Killings in 30 Years - Exit - Explaining Albania
Around 10,000 people have lost their lives to blood feuds in Albania since the fall of Communism. These are not crimes related to gangs or drugs, but rather to a centuries-old tradition that has wreaked havoc through communities for over 500 years. Blood feuds are present in many cultures- in...
But in general big cities have a high turnover of people moving to the city and/or leaving again, and a lot of people constantly interacting with people they don't know and probably will never meet again, and that definitely increases the chances of criminal behaviour.