If the DA is known to not charge crime, then people will not report crimes that occur because they believe it to be a waste of time. In the year after a special election to replace a DA for being too soft, I expect the crime rate to go up as people test if the new DA will actually take it seriously this time.
If it stays up for several years then I would see a problem, but all I'm seeing right now is the expected result of a forced regime change.
Where is your correlation now?
Or, maybe, just maybe, complex problems have complex causes and complex solutions.