Your main issue here is deciding what level of measurement and distribution your variables have - from there picking tests should be easy. Lab examined evidence yes/no would seem to be a nominal (and dichotomous) variable. Do the other variables have nominal, ordinal, interval or ratio levels of measurement, and are they continuous, discrete or count in nature? (I would guess that "arrest" and "DA referral" are also nominal/dichotomous, but charges could also be dichotomous or could be a count variable).
From there, a website like this can help you find the right test. E.g. if you want to see if there are differences between two groups of people (those with lab examined evidence and those without) on whether there was an arrest or not (assuming this is a nominal variable with 2 categories), you would use chi-squared test or Fisher's exact test.