My husband and I are looking for recommendations for sites that do the tenant background screenings for you (criminal history, evictions, debt in collection, etc...). I've seen quite a few posts on BP on this, but many are old and may be outdated, and there are none that I've seen that have specifically described if multi-state is included. 

Any suggestions would be greatly appreciated!

I used mysmartmove from BP as recently as May 2018. Nationwide eviction check, credit, criminal. $40, applicant pays so I don't even handle any money. Worked very quickly. But, I also did a prescreening of open source state court system, and contacted their landlord and employer prior to using My Smart Move.