@Jerome Kaidor
There is an adage that applies here:
Cheap, Fast, Good, Pick 2.
The vast majority of landlords/property managers want a criminal check, but it's not their primary concern (as opposed to credit, evictions etc). Most screening companies won't give you that level of county/state in depth search that will usually turn up most felonies, mainly because of cost , lack of demand, and marketplace knowledge.
Here's the issue: The multi state searches, and Intelius searches too (which are not FCRA compliant and can get you in real trouble,btw), are database searches. You can only have data in there that is able to be purchased or assembled from the state and local jurisdictions. So there's a ton that's missed.
The best way to do it is to check each county they lived in that comes back from the address trace. If you're incredibly paranoid you can do the counties adjacent, as well as counties worked in. If you're lucky they lived in one of the states that has a state level repository that is as reliable as a county level search.
Some states offer online searches, but even then it's not perfect. For example CT only offers data going back 7 years, so you have to know that and find someone who has older data.
I don't know that it would cost you $160 like @Kenneth LaVoie posted so many years ago, but it would be in the $50 and up range + court fees if there was no real volume. What you want basically is a criminal search equivalent to the ones done for managerial or mid level employment background checks and they're just not cheap. Remember you're putting boots on the ground to get a lot of the data.
Screening is an art and a science, good luck.